<PAGE>   1
 As filed with the Securities and Exchange Commission on December 23, 1999
                                                           Registration No. 333-
================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                              -------------------

                                    FORM S-8
                             REGISTRATION STATEMENT
                                      UNDER
                           THE SECURITIES ACT OF 1933

                              -------------------

                                GERON CORPORATION
             (Exact name of registrant as specified in its charter)

<TABLE>
<S>                                         <C>
        DELAWARE                                          75-2287752
(State of Incorporation)                    (I.R.S. Employer Identification No.)
</TABLE>

                              -------------------

                             230 CONSTITUTION DRIVE
                          MENLO PARK, CALIFORNIA 94025
                                 (650) 473-7700
                    (Address of principal executive offices)


                              -------------------

                             1992 STOCK OPTION PLAN
                        1996 DIRECTORS' STOCK OPTION PLAN
                            (Full title of the plans)


                                THOMAS B. OKARMA
                      PRESIDENT AND CHIEF EXECUTIVE OFFICER
                                GERON CORPORATION
                             230 CONSTITUTION DRIVE
                          MENLO PARK, CALIFORNIA 94025
                                 (650) 473-7700
            (Name, address, including zip code, and telephone number,
                   including area code, of agent for service)

                              -------------------

                                   Copies to:

                                ALAN C. MENDELSON
                                  ANDREA VACHSS
                               COOLEY GODWARD LLP
                               5 PALO ALTO SQUARE
                               3000 EL CAMINO REAL
                               PALO ALTO, CA 94306
                                 (650) 843-5000

                              -------------------

                         CALCULATION OF REGISTRATION FEE
<TABLE>
<CAPTION>
------------------------------------------------------------------------------------------------------------------------------------
                                                       Proposed Maximum           Proposed Maximum
Title of Securities                                        Offering                  Aggregate                 Amount of
 to be Registered        Amount to be Registered      Price per Share (1)        Offering Price (1)         Registration Fee
------------------------------------------------------------------------------------------------------------------------------------
<S>                             <C>                         <C>                      <C>                         <C>
Common Stock, par value         850,000 shares              $11.56                   $9,826,000                  $2600
    $.001 per share
------------------------------------------------------------------------------------------------------------------------------------
</TABLE>

(1)  Estimated solely for the purpose of calculating the amount of the
     registration fee pursuant to Rule 457(h). The price per share and aggregate
     offering price are based upon the average of the high and low prices of
     Registrant's Common Stock on December 21, 1999 as reported on the Nasdaq
     National Market.

<PAGE>   2

                 INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE

     The following documents filed by Geron Corporation (the "Company") with the
Securities and Exchange Commission are incorporated by reference into this
Registration Statement:

     (a) The Company's latest annual report on Form 10-K filed pursuant to
Sections 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended (the
"Exchange Act"), or either (1) the Company's latest prospectus filed pursuant to
Rule 424(b) under the Securities Act of 1933, as amended (the "Act"), that
contains audited financial statements for the Company's latest fiscal year for
which such statements have been filed, or (2) the Company's effective
registration statement on Form 10 or 20-F filed under the Exchange Act
containing audited financial statements for the Company's latest fiscal year.

     (b) All other reports filed pursuant to Sections 13(a) or 15(d) of the
Exchange Act since the end of the fiscal year covered by the annual reports, the
prospectus or the registration statement referred to in (a) above.

     (c) The description of the Company's Common Stock which is contained in a
registration statement filed under the Exchange Act, including any amendment or
report filed for the purpose of updating such description.

     All reports and other documents subsequently filed by the Company pursuant
to Sections 13(a), 13(c), 14 and 15(d) of the Exchange Act prior to the filing
of a post-effective amendment which indicates that all securities offered have
been sold or which deregisters all securities then remaining unsold, shall be
deemed to be incorporated by reference herein and to be a part of this
registration statement from the date of the filing of such reports and
documents.

                    INDEMNIFICATION OF DIRECTORS AND OFFICERS

     Section 145 of the Delaware General Corporation Law allows for the
indemnification of officers, directors, and other corporate agents in terms
sufficiently broad to indemnify these persons for liabilities (including
reimbursement for expenses incurred) arising under the Securities Act. The
registrant's certificate of incorporation and bylaws provide for indemnification
of the registrant's directors, officers, employees and other agents to the
extent and under the circumstances permitted by the Delaware General Corporation
Law. The registrant has also entered into agreements with its directors and
officers that will require the registrant, among other things, to indemnify them
against liabilities that may arise by reason of their status or service as
directors to the fullest extent not prohibited by law. In addition, the
registrant carries director and officer liability insurance.


                                       1.

<PAGE>   3



                                    EXHIBITS

<TABLE>
<CAPTION>
EXHIBIT
NUMBER
    <S>     <C>
     5      Opinion of Cooley Godward LLP
    23.1    Consent of Ernst & Young LLP, Independent Auditors
    23      Consent of Arthur Andersen, Independent Public Accountants
    23.2    Consent of Cooley Godward LLP is contained in Exhibit 5 to this Registration Statement
    24      Power of Attorney is contained on the signature pages.
    99.1    1992 Stock Option Plan, as amended
    99.2    1996 Directors' Stock Option Plan, as amended
</TABLE>

                                  UNDERTAKINGS

     The undersigned registrant hereby undertakes:

     (1) To file, during any period in which offers or sales are being made, a
post-effective amendment to this registration statement to include any material
information with respect to the plan of distribution not previously disclosed in
the registration statement or any material change to that information in the
registration statement.

     (2) That, for the purpose of determining any liability under the Securities
Act, each post-effective amendment shall be deemed to be a new registration
statement relating to the securities it offers, and the offering of the
securities at that time shall be deemed to be the initial bona fide offering
thereof.

     (3) To remove from registration by means of a post-effective amendment any
of the securities being registered which remain unsold at the termination of
this offering.

     (4) That, for purposes of determining any liability under the Securities
Act, each filing of the registrant's annual report pursuant to Section 13(a) or
Section 15(d) of the Exchange Act that is incorporated by reference in the
registration statement shall be deemed to be a new registration statement
relating to the securities offered therein, and the offering of the securities
at that time shall be deemed to be the initial bona fide offering thereof.

     Insofar as indemnification for liabilities arising under the Securities Act
may be permitted to directors, officers and controlling persons of the
registrant pursuant to the foregoing provisions, or otherwise, the registrant
has been advised that in the opinion of the SEC this form of indemnification is
against public policy as expressed in the Securities Act and is, therefore,
unenforceable. In the event that a claim for indemnification against these
liabilities (other than the payment by the registrant of expenses incurred or
paid by a director, officer or controlling person of the registrant in the
successful defense of any action, suit or proceeding) is asserted by a director,
officer or controlling person in connection with the securities being
registered, the registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of this issue.

                                       2.

<PAGE>   4



                                   SIGNATURES

     Pursuant to the requirements of the Securities Act of 1933, as amended,
Geron Corporation certifies that it has reasonable grounds to believe that it
meets all of the requirements for filing on Form S-8 and has duly caused this
registration statement to be signed on its behalf by the undersigned, thereunto
duly authorized, in the City of Menlo Park, State of California, on December 22,
1999.

                                       GERON CORPORATION


                                       By: /s/ David L. Greenwood
                                           ----------------------
                                           David L. Greenwood
                                           Chief Financial Officer

                                       3.

<PAGE>   5



                                POWER OF ATTORNEY

     KNOW ALL PERSONS BY THESE PRESENTS, that each person whose signature
appears below hereby constitutes and appoints Thomas B. Okarma and David L.
Greenwood, jointly and severally, his or her true and lawful attorneys-in-fact,
each with full power of substitution, for him or her in any and all capacities,
to sign any and all amendments (including post-effective amendments) to this
Registration Statement, and to file the same, with all exhibits thereto, and
other documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents, and each of them,
full power and authority to do and perform each and every act and thing
requisite and necessary to be done in connection therewith, as fully to all
intents and purposes as he might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents, or any of them, or their
or his substitutes or substitute, may lawfully do or cause to be done by virtue
hereof.

     Pursuant to the requirements of the Securities Act of 1933, this
registration statement has been signed by the following persons in the
capacities and on the dates indicated.

<TABLE>
<CAPTION>
       SIGNATURE                                        TITLE                                    DATE
       ---------                                        -----                                    ----
<S>                                    <C>                                                <C>
/s/ Thomas B. Okarma                   President, Chief Executive Officer                 December 22, 1999
---------------------------            and Director
Thomas B. Okarma


/s/ David L. Greenwood                 Vice President and Chief Financial Officer         December 22, 1999
---------------------------            (Principal Financial and Accounting Officer)
David L. Greenwood

/s/ Alexander E. Barkas                Director                                           December 22, 1999
---------------------------
Alexander E. Barkas

/s/ Ronald W. Eastman                  Director                                           December 22, 1999
---------------------------
Ronald W. Eastman

                                       Director                                           December __, 1999
---------------------------
Edward V. Fritzky

/s/ Thomas D. Kiley                    Director                                           December 22, 1999
---------------------------
Thomas D. Kiley


---------------------------            Director                                           December __, 1999
Gary L. Neil


---------------------------            Director                                           December __, 1999
Robert B. Stein


---------------------------            Director                                           December __, 1999
John P. Walker
</TABLE>

                                       4.

<PAGE>   6



                                  EXHIBIT INDEX
<TABLE>
<CAPTION>
EXHIBIT                                                                                       SEQUENTIAL PAGE
NUMBER                                       DESCRIPTION                                         NUMBERS
 <S>         <C>
  5          Opinion of Cooley Godward LLP
 23.1        Consent of Ernst & Young LLP, Independent Auditors
 23.2        Consent of Arthur Andersen, Independent Public Accountants
 23.3        Consent  of  Cooley   Godward  LLP  is   contained  in  Exhibit 5  to  this
             Registration Statement
 24          Power of Attorney is contained on the signature pages.
 99.1        1992 Stock Option Plan, as amended
 99.2        1996 Directors' Stock Option Plan, as amended
</TABLE>

                                       5.
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 14413}]
{"company-data": {"conformed-name": "GERON CORPORATION", "cik": "0000886744", "assigned-sic": "2834", "irs-number": "752287752", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-93527", "film-number": "99779937"}, "business-address": {"street1": "230 CONSTITUTION DRIVE", "city": "MENLO PARK", "state": "CA", "zip": "94025", "phone": "6504737700"}, "mail-address": {"street1": "200 CONSTITUTION DRIVE", "city": "MENLO PARK", "state": "CA", "zip": "94025"}}
1
 As filed with the Securities and Exchange Commission on December 23, 1999
                                                           Registration No. 333-
================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                              -------------------

                                    FORM S-8
                             REGISTRATION STATEMENT
                                      UNDER
                           THE SECURITIES ACT OF 1933

                              -------------------

                                GERON CORPORATION
             (Exact name of registrant as specified in its charter)
DELAWARE                                          75-2287752
(State of Incorporation)                    (I.R.S. Employer Identification No.)
-------------------

                             230 CONSTITUTION DRIVE
                          MENLO PARK, CALIFORNIA 94025
                                 (650) 473-7700
                    (Address of principal executive offices)

                              -------------------

                             1992 STOCK OPTION PLAN
                        1996 DIRECTORS' STOCK OPTION PLAN
                            (Full title of the plans)

                                THOMAS B. OKARMA
                      PRESIDENT AND CHIEF EXECUTIVE OFFICER
                                GERON CORPORATION
                             230 CONSTITUTION DRIVE
                          MENLO PARK, CALIFORNIA 94025
                                 (650) 473-7700
            (Name, address, including zip code, and telephone number,
                   including area code, of agent for service)

                              -------------------

                                   Copies to:

                                ALAN C. MENDELSON
                                  ANDREA VACHSS
                               COOLEY GODWARD LLP
                               5 PALO ALTO SQUARE
                               3000 EL CAMINO REAL
                               PALO ALTO, CA 94306
                                 (650) 843-5000

                              -------------------

                         CALCULATION OF REGISTRATION FEE
------------------------------------------------------------------------------------------------------------------------------------
                                                       Proposed Maximum           Proposed Maximum
Title of Securities                                        Offering                  Aggregate                 Amount of
 to be Registered        Amount to be Registered      Price per Share (1)        Offering Price (1)         Registration Fee
------------------------------------------------------------------------------------------------------------------------------------
Common Stock, par value         850,000 shares              $11.56                   $9,826,000                  $2600
    $.001 per share
------------------------------------------------------------------------------------------------------------------------------------
(1)  Estimated solely for the purpose of calculating the amount of the
     registration fee pursuant to Rule 457(h). The price per share and aggregate
     offering price are based upon the average of the high and low prices of
     Registrant's Common Stock on December 21, 1999 as reported on the Nasdaq
     National Market.
2

                 INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE

     The following documents filed by Geron Corporation (the "Company") with the
Securities and Exchange Commission are incorporated by reference into this
Registration Statement:

     (a) The Company's latest annual report on Form 10-K filed pursuant to
Sections 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended (the
"Exchange Act"), or either (1) the Company's latest prospectus filed pursuant to
Rule 424(b) under the Securities Act of 1933, as amended (the "Act"), that
contains audited financial statements for the Company's latest fiscal year for
which such statements have been filed, or (2) the Company's effective
registration statement on Form 10 or 20-F filed under the Exchange Act
containing audited financial statements for the Company's latest fiscal year.

     (b) All other reports filed pursuant to Sections 13(a) or 15(d) of the
Exchange Act since the end of the fiscal year covered by the annual reports, the
prospectus or the registration statement referred to in (a) above.

     (c) The description of the Company's Common Stock which is contained in a
registration statement filed under the Exchange Act, including any amendment or
report filed for the purpose of updating such description.

     All reports and other documents subsequently filed by the Company pursuant
to Sections 13(a), 13(c), 14 and 15(d) of the Exchange Act prior to the filing
of a post-effective amendment which indicates that all securities offered have
been sold or which deregisters all securities then remaining unsold, shall be
deemed to be incorporated by reference herein and to be a part of this
registration statement from the date of the filing of such reports and
documents.

                    INDEMNIFICATION OF DIRECTORS AND OFFICERS

     Section 145 of the Delaware General Corporation Law allows for the
indemnification of officers, directors, and other corporate agents in terms
sufficiently broad to indemnify these persons for liabilities (including
reimbursement for expenses incurred) arising under the Securities Act. The
registrant's certificate of incorporation and bylaws provide for indemnification
of the registrant's directors, officers, employees and other agents to the
extent and under the circumstances permitted by the Delaware General Corporation
Law. The registrant has also entered into agreements with its directors and
officers that will require the registrant, among other things, to indemnify them
against liabilities that may arise by reason of their status or service as
directors to the fullest extent not prohibited by law. In addition, the
registrant carries director and officer liability insurance.

                                       1.
3

                                    EXHIBITS
EXHIBIT
NUMBER
5      Opinion of Cooley Godward LLP
    23.1    Consent of Ernst & Young LLP, Independent Auditors
    23      Consent of Arthur Andersen, Independent Public Accountants
    23.2    Consent of Cooley Godward LLP is contained in Exhibit 5 to this Registration Statement
    24      Power of Attorney is contained on the signature pages.
    99.1    1992 Stock Option Plan, as amended
    99.2    1996 Directors' Stock Option Plan, as amended
UNDERTAKINGS

     The undersigned registrant hereby undertakes:

     (1) To file, during any period in which offers or sales are being made, a
post-effective amendment to this registration statement to include any material
information with respect to the plan of distribution not previously disclosed in
the registration statement or any material change to that information in the
registration statement.

     (2) That, for the purpose of determining any liability under the Securities
Act, each post-effective amendment shall be deemed to be a new registration
statement relating to the securities it offers, and the offering of the
securities at that time shall be deemed to be the initial bona fide offering
thereof.

     (3) To remove from registration by means of a post-effective amendment any
of the securities being registered which remain unsold at the termination of
this offering.

     (4) That, for purposes of determining any liability under the Securities
Act, each filing of the registrant's annual report pursuant to Section 13(a) or
Section 15(d) of the Exchange Act that is incorporated by reference in the
registration statement shall be deemed to be a new registration statement
relating to the securities offered therein, and the offering of the securities
at that time shall be deemed to be the initial bona fide offering thereof.

     Insofar as indemnification for liabilities arising under the Securities Act
may be permitted to directors, officers and controlling persons of the
registrant pursuant to the foregoing provisions, or otherwise, the registrant
has been advised that in the opinion of the SEC this form of indemnification is
against public policy as expressed in the Securities Act and is, therefore,
unenforceable. In the event that a claim for indemnification against these
liabilities (other than the payment by the registrant of expenses incurred or
paid by a director, officer or controlling person of the registrant in the
successful defense of any action, suit or proceeding) is asserted by a director,
officer or controlling person in connection with the securities being
registered, the registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of this issue.

                                       2.
4

                                   SIGNATURES

     Pursuant to the requirements of the Securities Act of 1933, as amended,
Geron Corporation certifies that it has reasonable grounds to believe that it
meets all of the requirements for filing on Form S-8 and has duly caused this
registration statement to be signed on its behalf by the undersigned, thereunto
duly authorized, in the City of Menlo Park, State of California, on December 22,
1999.

                                       GERON CORPORATION

                                       By: /s/ David L. Greenwood
                                           ----------------------
                                           David L. Greenwood
                                           Chief Financial Officer

                                       3.
5

                                POWER OF ATTORNEY

     KNOW ALL PERSONS BY THESE PRESENTS, that each person whose signature
appears below hereby constitutes and appoints Thomas B. Okarma and David L.
Greenwood, jointly and severally, his or her true and lawful attorneys-in-fact,
each with full power of substitution, for him or her in any and all capacities,
to sign any and all amendments (including post-effective amendments) to this
Registration Statement, and to file the same, with all exhibits thereto, and
other documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents, and each of them,
full power and authority to do and perform each and every act and thing
requisite and necessary to be done in connection therewith, as fully to all
intents and purposes as he might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents, or any of them, or their
or his substitutes or substitute, may lawfully do or cause to be done by virtue
hereof.

     Pursuant to the requirements of the Securities Act of 1933, this
registration statement has been signed by the following persons in the
capacities and on the dates indicated.
SIGNATURE                                        TITLE                                    DATE
       ---------                                        -----                                    ----
/s/ Thomas B. Okarma                   President, Chief Executive Officer                 December 22, 1999
---------------------------            and Director
Thomas B. Okarma

/s/ David L. Greenwood                 Vice President and Chief Financial Officer         December 22, 1999
---------------------------            (Principal Financial and Accounting Officer)
David L. Greenwood

/s/ Alexander E. Barkas                Director                                           December 22, 1999
---------------------------
Alexander E. Barkas

/s/ Ronald W. Eastman                  Director                                           December 22, 1999
---------------------------
Ronald W. Eastman

                                       Director                                           December __, 1999
---------------------------
Edward V. Fritzky

/s/ Thomas D. Kiley                    Director                                           December 22, 1999
---------------------------
Thomas D. Kiley

---------------------------            Director                                           December __, 1999
Gary L. Neil

---------------------------            Director                                           December __, 1999
Robert B. Stein

---------------------------            Director                                           December __, 1999
John P. Walker
4.
6

                                  EXHIBIT INDEX
EXHIBIT                                                                                       SEQUENTIAL PAGE
NUMBER                                       DESCRIPTION                                         NUMBERS
5          Opinion of Cooley Godward LLP
 23.1        Consent of Ernst & Young LLP, Independent Auditors
 23.2        Consent of Arthur Andersen, Independent Public Accountants
 23.3        Consent  of  Cooley   Godward  LLP  is   contained  in  Exhibit 5  to  this
             Registration Statement
 24          Power of Attorney is contained on the signature pages.
 99.1        1992 Stock Option Plan, as amended
 99.2        1996 Directors' Stock Option Plan, as amended
5.