<PAGE>   1
================================================================================

                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

                              ---------------------
                                    FORM S-8

                          REGISTRATION STATEMENT UNDER
                           THE SECURITIES ACT OF 1933

                              CAMPBELL SOUP COMPANY
               (Exact Name of Issuer As Specified in Its Charter)

     NEW JERSEY                                         21-0419870
State of Incorporation                        I.R.S. Employer Identification No.

                                 CAMPBELL PLACE
                          CAMDEN, NEW JERSEY 08103-1799
                           Principal Executive Offices

               CAMPBELL SOUP COMPANY 1994 LONG-TERM INCENTIVE PLAN
                            (FULL TITLE OF THE PLAN)

                                ELLEN ORAN KADEN
               SENIOR VICE PRESIDENT - LAW AND GOVERNMENT AFFAIRS
                              CAMPBELL SOUP COMPANY
                  CAMPBELL PLACE, CAMDEN, NEW JERSEY 08103-1799
                      Name and address of agent for service

   TELEPHONE NUMBER, INCLUDING AREA CODE, OF AGENT FOR SERVICE: (856) 342-4800

                         CALCULATION OF REGISTRATION FEE

<TABLE>
<CAPTION>
                                                                           PROPOSED
                                                    PROPOSED               MAXIMUM
                                                    MAXIMUM               AGGREGATE
TITLE OF SECURITIES TO       AMOUNT TO BE        OFFERING PRICE           OFFERING(1)                   AMOUNT OF
     BE REGISTERED            REGISTERED           PER UNIT(1)              PRICE                    REGISTRATION FEE
----------------------       ------------        --------------           -----------                ----------------
<S>                          <C>                 <C>                      <C>                       <C>
CAPITAL STOCK, PAR            25,000,000             $31.688              $792,200,000                $209,140.80
VALUE $.075 PER SHARE
</TABLE>

(1) The amounts are based upon the average of the high and low sale prices for
the capital stock as reported on the New York Stock Exchange on May 26, 2000,
and are used solely for the purpose of calculating the registration fee in
accordance with paragraphs (c) and (h) of Rule 457 under the Securities Act of
1933.
<PAGE>   2
PART II

INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

Item 3.    Incorporation of Documents by Reference

           The Registrant and the Campbell Soup Company 1994 Long-Term Incentive
Plan incorporate by reference into the registration statement the documents
listed below:

           (a) Registrant's annual report on Form 10-K for the fiscal year ended
August 1, 1999.

           (b) All other reports filed by the Registrant pursuant to Section 13
(a) or 15(d) of the Securities Exchange Act of 1934 since August 1, 1999.

           (c) The description of the capital stock contained in Campbell's
Registration Statement dated November 16, 1954, filed under the Securities
Exchange Act of 1934, including any amendment or report filed for the purpose of
updating such description.

           (d) The contents of Registration Statement on Form S-8, SEC File No.
33-56899 for the Campbell Soup Company 1994 Long-Term Incentive Plan.

           All documents subsequently filed by the Registrant pursuant to
Sections 13(a), 13(c), 14 and 15(d) of the Securities Exchange Act of 1934,
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 in this
Registration Statement and to be a part hereof from the date of filing of such
documents.

Item 4.    Description of Securities

           The securities to be offered are registered under Section 12 of the
Exchange Act. Pursuant to Section 4.3 of the Campbell Soup Company 1994
Long-Term Incentive Plan, the shares to be offered must be capital stock
previously issued and outstanding and reacquired by the Registrant.

Item 5.    Interest of Named Experts

           Not Applicable.

Item 6.    Indemnification of Directors and Officers

           The Registrant's By-Laws and Section 14A:3-5 of the New Jersey
Business Corporation Act provide for limitation of liability and indemnification
of the Registrant's directors and officers in a variety of circumstances, which
may include liabilities under the Securities Act of 1933. In addition, the
Registrant has purchased insurance permitted by New Jersey on behalf of
directors, officers, employees or agents which may cover liabilities under the
Securities Act of 1933.
<PAGE>   3
Item 7.    Exemption From Registration Claimed

           Not Applicable.

Item 8.    Exhibits

            4     -        Campbell Soup Company 1994 Long-Term Incentive Plan

           23     -        Consent of PricewaterhouseCoopers LLP

           24     -        Power of Attorney

Item 9.    Undertakings

(a)        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:

           (i) To include any prospectus required by Section 10(a)(3) of the
Securities Act of 1933;

           (ii) To reflect in the prospectus any facts or events arising after
the effective date of the Registration Statement (or the most recent
post-effective amendment thereof) which, individually or in the aggregate,
represent a fundamental change in the information set forth in the registration
statement. Notwithstanding the foregoing, any increase or decrease in volume of
securities offered (if the total dollar value of securities offered would not
exceed that which was registered) and any deviation from the low or high end of
the estimated maximum offering range may be reflected in the form of a
prospectus filed with the Commission pursuant to Rule 424(b) if, in the
aggregate, the changes in volume and price represent no more than a 20 percent
change in the maximum aggregate offering price set forth in the "Calculation of
Registration Fee" table in the effective registration statement;

           (iii) To include any material information with respect to the plan of
distribution not previously disclosed in the Registration Statement or any
material change to such information in the Registration Statement;

                  provided, however, that paragraphs (a)(1)(i) and (a)(1)(ii) do
not apply if the Registration Statement is on Form S-3 or Form S-8, and the
information required to be included in a post-effective amendment by those
paragraphs is contained in periodic reports filed by the Registrant pursuant to
Section 13 or Section 15(d) of the Securities Exchange Act of 1934 that are
incorporated by reference in the Registration Statement.

           (2) That, for the purpose of determining any liability under the
Securities Act of 1933, each such post-effective amendment shall be deemed to be
a new registration statement relating to the securities offered therein, and the
offering of such securities at that time shall be deemed to be the initial bona
fide offering thereof.
<PAGE>   4
           (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 the offering.

(b) The undersigned Registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of 1933, each filing of the
Registrant's annual report pursuant to Section 13(a) or 15(d) of the Securities
Exchange Act of 1934 (and, where applicable, each filing of an employee benefit
plan's annual report pursuant to Section 15(d) of the Securities Exchange Act of
1934) 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 such securities at that time shall be deemed to be
the initial bona fide offering thereof.

(c) Insofar as indemnification for liabilities arising under the Securities Act
of 1933 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 Securities and Exchange Commission
such indemnification is against public policy as expressed in the Act and is,
therefore, unenforceable. In the event that a claim for indemnification against
such 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 such
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 Act and will be governed by the final adjudication of
such issue.
<PAGE>   5
                                   SIGNATURES

Pursuant to the requirements of the Securities Act of 1933, the Registrant
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 Camden and State of New Jersey, on the 2nd day of
June 2000.

                                                 CAMPBELL SOUP COMPANY

                                                 BY: /s/ Basil L. Anderson
                                                     ---------------------
                                                     Basil L. Anderson
                                                     Executive Vice President
                                                     and Chief Financial Officer

Philip E. Lippincott*             Chairman and Director
David W. Johnson*                 President, Chief Executive
                                  Officer and Director
Alva A. App*                      Director
Edmund M. Carpenter*              Director
Bennett Dorrance*                 Director
Thomas W. Field, Jr.*             Director
Kent B. Foster*                   Director
Harvey Golub*                     Director
David K.P. Li*                    Director
Mary Alice D. Malone*             Director
Charles H. Mott*                  Director
Charles R. Perrin*                Director
George M. Sherman*                Director
Donald M. Stewart*                Director
George Strawbridge, Jr.*          Director
Charlotte C. Weber*               Director


* This Registration Statement has been duly signed by the undersigned as
attorney-in-fact on behalf of each person so indicated pursuant to a
power-of-attorney duly executed by each such person.


                                                          /s/ John J. Furey
                                                          ----------------------
                                                          John J. Furey
                                                          Attorney-in-fact
<PAGE>   6
                                INDEX OF EXHIBITS

<TABLE>
<CAPTION>
DOCUMENT
--------
<S>          <C>
    4        Campbell Soup Company 1994 Long-Term Incentive Plan

   23        Consent of PricewaterhouseCoopers LLP

   24        Power of Attorney
</TABLE>
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{"company-data": {"conformed-name": "CAMPBELL SOUP CO", "cik": "0000016732", "assigned-sic": "2000", "irs-number": "210419870", "state-of-incorporation": "NJ", "fiscal-year-end": "0729"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-38520", "film-number": "648749"}, "business-address": {"street1": "CAMPBELL PL", "city": "CAMDEN", "state": "NJ", "zip": "08103", "phone": "6093424800"}, "mail-address": {"street1": "CAMPBELL PL", "city": "CAMDEN", "state": "NJ", "zip": "08103"}}
1
================================================================================

                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

                              ---------------------
                                    FORM S-8

                          REGISTRATION STATEMENT UNDER
                           THE SECURITIES ACT OF 1933

                              CAMPBELL SOUP COMPANY
               (Exact Name of Issuer As Specified in Its Charter)

     NEW JERSEY                                         21-0419870
State of Incorporation                        I.R.S. Employer Identification No.

                                 CAMPBELL PLACE
                          CAMDEN, NEW JERSEY 08103-1799
                           Principal Executive Offices

               CAMPBELL SOUP COMPANY 1994 LONG-TERM INCENTIVE PLAN
                            (FULL TITLE OF THE PLAN)

                                ELLEN ORAN KADEN
               SENIOR VICE PRESIDENT - LAW AND GOVERNMENT AFFAIRS
                              CAMPBELL SOUP COMPANY
                  CAMPBELL PLACE, CAMDEN, NEW JERSEY 08103-1799
                      Name and address of agent for service

   TELEPHONE NUMBER, INCLUDING AREA CODE, OF AGENT FOR SERVICE: (856) 342-4800

                         CALCULATION OF REGISTRATION FEE
PROPOSED
                                                    PROPOSED               MAXIMUM
                                                    MAXIMUM               AGGREGATE
TITLE OF SECURITIES TO       AMOUNT TO BE        OFFERING PRICE           OFFERING(1)                   AMOUNT OF
     BE REGISTERED            REGISTERED           PER UNIT(1)              PRICE                    REGISTRATION FEE
----------------------       ------------        --------------           -----------                ----------------
CAPITAL STOCK, PAR            25,000,000             $31.688              $792,200,000                $209,140.80
VALUE $.075 PER SHARE
(1) The amounts are based upon the average of the high and low sale prices for
the capital stock as reported on the New York Stock Exchange on May 26, 2000,
and are used solely for the purpose of calculating the registration fee in
accordance with paragraphs (c) and (h) of Rule 457 under the Securities Act of
1933.
2
PART II

INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

Item 3.    Incorporation of Documents by Reference

           The Registrant and the Campbell Soup Company 1994 Long-Term Incentive
Plan incorporate by reference into the registration statement the documents
listed below:

           (a) Registrant's annual report on Form 10-K for the fiscal year ended
August 1, 1999.

           (b) All other reports filed by the Registrant pursuant to Section 13
(a) or 15(d) of the Securities Exchange Act of 1934 since August 1, 1999.

           (c) The description of the capital stock contained in Campbell's
Registration Statement dated November 16, 1954, filed under the Securities
Exchange Act of 1934, including any amendment or report filed for the purpose of
updating such description.

           (d) The contents of Registration Statement on Form S-8, SEC File No.
33-56899 for the Campbell Soup Company 1994 Long-Term Incentive Plan.

           All documents subsequently filed by the Registrant pursuant to
Sections 13(a), 13(c), 14 and 15(d) of the Securities Exchange Act of 1934,
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 in this
Registration Statement and to be a part hereof from the date of filing of such
documents.

Item 4.    Description of Securities

           The securities to be offered are registered under Section 12 of the
Exchange Act. Pursuant to Section 4.3 of the Campbell Soup Company 1994
Long-Term Incentive Plan, the shares to be offered must be capital stock
previously issued and outstanding and reacquired by the Registrant.

Item 5.    Interest of Named Experts

           Not Applicable.

Item 6.    Indemnification of Directors and Officers

           The Registrant's By-Laws and Section 14A:3-5 of the New Jersey
Business Corporation Act provide for limitation of liability and indemnification
of the Registrant's directors and officers in a variety of circumstances, which
may include liabilities under the Securities Act of 1933. In addition, the
Registrant has purchased insurance permitted by New Jersey on behalf of
directors, officers, employees or agents which may cover liabilities under the
Securities Act of 1933.
3
Item 7.    Exemption From Registration Claimed

           Not Applicable.

Item 8.    Exhibits

            4     -        Campbell Soup Company 1994 Long-Term Incentive Plan

           23     -        Consent of PricewaterhouseCoopers LLP

           24     -        Power of Attorney

Item 9.    Undertakings

(a)        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:

           (i) To include any prospectus required by Section 10(a)(3) of the
Securities Act of 1933;

           (ii) To reflect in the prospectus any facts or events arising after
the effective date of the Registration Statement (or the most recent
post-effective amendment thereof) which, individually or in the aggregate,
represent a fundamental change in the information set forth in the registration
statement. Notwithstanding the foregoing, any increase or decrease in volume of
securities offered (if the total dollar value of securities offered would not
exceed that which was registered) and any deviation from the low or high end of
the estimated maximum offering range may be reflected in the form of a
prospectus filed with the Commission pursuant to Rule 424(b) if, in the
aggregate, the changes in volume and price represent no more than a 20 percent
change in the maximum aggregate offering price set forth in the "Calculation of
Registration Fee" table in the effective registration statement;

           (iii) To include any material information with respect to the plan of
distribution not previously disclosed in the Registration Statement or any
material change to such information in the Registration Statement;

                  provided, however, that paragraphs (a)(1)(i) and (a)(1)(ii) do
not apply if the Registration Statement is on Form S-3 or Form S-8, and the
information required to be included in a post-effective amendment by those
paragraphs is contained in periodic reports filed by the Registrant pursuant to
Section 13 or Section 15(d) of the Securities Exchange Act of 1934 that are
incorporated by reference in the Registration Statement.

           (2) That, for the purpose of determining any liability under the
Securities Act of 1933, each such post-effective amendment shall be deemed to be
a new registration statement relating to the securities offered therein, and the
offering of such securities at that time shall be deemed to be the initial bona
fide offering thereof.
4
           (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 the offering.

(b) The undersigned Registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of 1933, each filing of the
Registrant's annual report pursuant to Section 13(a) or 15(d) of the Securities
Exchange Act of 1934 (and, where applicable, each filing of an employee benefit
plan's annual report pursuant to Section 15(d) of the Securities Exchange Act of
1934) 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 such securities at that time shall be deemed to be
the initial bona fide offering thereof.

(c) Insofar as indemnification for liabilities arising under the Securities Act
of 1933 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 Securities and Exchange Commission
such indemnification is against public policy as expressed in the Act and is,
therefore, unenforceable. In the event that a claim for indemnification against
such 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 such
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 Act and will be governed by the final adjudication of
such issue.
5
                                   SIGNATURES

Pursuant to the requirements of the Securities Act of 1933, the Registrant
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 Camden and State of New Jersey, on the 2nd day of
June 2000.

                                                 CAMPBELL SOUP COMPANY

                                                 BY: /s/ Basil L. Anderson
                                                     ---------------------
                                                     Basil L. Anderson
                                                     Executive Vice President
                                                     and Chief Financial Officer

Philip E. Lippincott*             Chairman and Director
David W. Johnson*                 President, Chief Executive
                                  Officer and Director
Alva A. App*                      Director
Edmund M. Carpenter*              Director
Bennett Dorrance*                 Director
Thomas W. Field, Jr.*             Director
Kent B. Foster*                   Director
Harvey Golub*                     Director
David K.P. Li*                    Director
Mary Alice D. Malone*             Director
Charles H. Mott*                  Director
Charles R. Perrin*                Director
George M. Sherman*                Director
Donald M. Stewart*                Director
George Strawbridge, Jr.*          Director
Charlotte C. Weber*               Director

* This Registration Statement has been duly signed by the undersigned as
attorney-in-fact on behalf of each person so indicated pursuant to a
power-of-attorney duly executed by each such person.

                                                          /s/ John J. Furey
                                                          ----------------------
                                                          John J. Furey
                                                          Attorney-in-fact
6
                                INDEX OF EXHIBITS
DOCUMENT
--------
4        Campbell Soup Company 1994 Long-Term Incentive Plan

   23        Consent of PricewaterhouseCoopers LLP

   24        Power of Attorney