<PAGE>   1
   As filed with the Securities and Exchange Commission on September 18, 1998
                                                           Registration No. 333-

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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

                                STERLING BANCORP
             (Exact name of registrant as specified in its charter)

          NEW YORK                                             13-2565216
(State or other jurisdiction of                             (I.R.S. Employer
incorporation or organization)                            Identification Number)

                                 430 Park Avenue
                          New York, New York 10022-3505
                                 (212) 826-8000
                        (Address, including zip code, and
                     telephone number, including area code,
                         of principal executive offices)

                      STERLING BANCORP STOCK INCENTIVE PLAN
                            (Full title of the plan)

                              Jerrold Gilbert, Esq.
             Executive Vice President, General Counsel and Secretary
                                Sterling Bancorp
                                 430 Park Avenue
                          New York, New York 10022-3505
                                 (212) 826-8044
            (Name, address, including zip code, and telephone number,
                   including area code, of agent for service)

                                    Copies to
                             Michael J. Segal, Esq.
                      Paul Weiss Rifkind Wharton & Garrison
                           1285 Avenue of the Americas
                               New York, NY 10019
                                 (212) 373-3000

                         CALCULATION OF REGISTRATION FEE
<TABLE>
<CAPTION>
-------------------------------------------------------- ------------------------ ----------------- ----------------- --------------
                  Title Of Securities                            Amount           Proposed Maximum      Proposed           Amount
                         To Be                                    To Be            Offering Price       Maximum              Of
                      Registered                               Registered          Per Share (1)       Aggregate        Registration
                                                                                                        Offering            Fee
                                                                                                         Price
-------------------------------------------------------- ------------------------ ----------------- ----------------- --------------
<S>                                                      <C>                      <C>               <C>               <C>
Common Stock $1.00 Par Value (including associated and           400,000              $20.875          $8,350,000        $2,463.25
attached rights to purchase shares of capital stock
under the Company's Shareholder Protection Rights
Agreement dated as of May 21, 1998.
======================================================== ======================== ================= ================= ==============
</TABLE>

(1) Estimated solely for calculating the amount of the registration fee,
pursuant to Rule 457(h) under the Securities Act of 1933 (the "Securities Act")
based upon the average of the high and low sales prices of the Common Shares as
reported by the New York Stock Exchange on September 15, 1998.
<PAGE>   2
                                     PART II

Item 3.  INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE

         The following documents, filed with the Securities and Exchange
Commission (the "Commission") by Sterling Bancorp, a New York corporation (the
"Company"), are incorporated herein by reference:

(a)      The Company's Annual Report on Form 10-K for the fiscal year ended
         December 31, 1997 (File No. 001-05273), filed pursuant to the
         Securities Exchange Act of 1934, as amended (the "Exchange Act");

(b)      The Company's Quarterly Reports on Form 10-Q for the quarters ended
         March 31, 1998 and June 30, 1998 (File No. 001-05273), filed pursuant
         to the Exchange Act;

(c)      The Company's Current Report on Form 8-K filed on June 5, 1998 (File
         No. 001-05273), pursuant to the Exchange Act;

(d)      The Company's Registration Statement on Form S-8 filed on May 20, 1997
         (File No. 333-27473), pursuant to the Securities Act; and

(e)      The description of the Company's Common Stock, $1.00 par value,
         contained in the Company's Registration Statement filed under the
         Exchange Act, including all amendments or reports filed for the purpose
         of updating such description, and the description of rights associated
         and attached to the Common Stock ("Rights") to purchase the Company's
         Series E Preferred Shares, $5.00 par value ("Preferred Shares"), or
         fractions thereof, at a Purchase Price of $100.00 per one one-hundredth
         of a Preferred Share, contained in the Company's Registration Statement
         therefor filed under the Exchange Act on June 15, 1998, including all
         amendments or reports filed for the purpose of updating such
         description.

         All documents subsequently filed by the Company with the Commission
pursuant to Sections 13(a), 13(c), 14 or 15(d) of the Exchange Act subsequent to
the date of this Registration Statement and prior to the filing of a
post-effective amendment which indicates that all securities offered hereby have
been sold or which deregisters all securities then remaining unsold shall be
deemed to be incorporated herein by reference and to be a part hereof from the
date of the filing of such documents with the Commission.
<PAGE>   3
Item 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL

An opinion on the validity of the securities being registered hereunder has been
given by Jerrold Gilbert, Esq., General Counsel of the Company. Mr. Gilbert
holds options to purchase 42,000 Common Shares, with attached and associated
Rights, being registered hereunder.

Item 8.  EXHIBITS

5        Opinion of Jerrold Gilbert, Esq. as to the validity of the shares to be
         issued.

23.1     Consent of KPMG Peat Marwick LLP.

23.2     Consent of Jerrold Gilbert, Esq. (contained in Exhibit 5).

24       Power of Attorney (reference is made to the signature page).
<PAGE>   4
                                   SIGNATURES

         Pursuant to the requirements of the Securities Act, the Company
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 New York, State of New York, on the 20th day of
August, 1998.

                                STERLING BANCORP



                                             By: /s/ Louis J. Cappelli
                                                     Louis J. Cappelli
                                                     Chairman of the Board and
                                                     Chief Executive Officer

         KNOW ALL MEN BY THESE PRESENTS, that each person whose signature
appears below constitutes and appoints Louis J. Cappelli, John C. Millman and
Jerrold Gilbert his true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities, to sign any and all amendments to this registration and
to file the same, with exhibits thereto, and other documents in connection
therewith with the Commission, granting unto said attorney-in-fact and agent
full power and authority to do and perform each and every act and thing
requisite and necessary to be done, as fully to all intents and purposes as he
might or could do in person, hereby ratifying and confirming all that said
attorney-in-fact and agent or any of them, or their or his substitute or
substitutes, may lawfully do or cause to be done by virtue hereof.

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

<TABLE>
<CAPTION>
                Signature                                    Title                                Date
                ---------                                    -----                                ----

<S>                                         <C>                                              <C>
/s/Louis J. Cappelli                        Chairman of the Board,                           August 20, 1998
---------------------------                 Chief Executive Officer
Louis J. Cappelli                           and Director


/s/John C. Millman                          President and Director                           August 20, 1998
------------------
John C. Millman
</TABLE>
<PAGE>   5
<TABLE>
<CAPTION>
<S>                                         <C>                                              <C>
/s/John W. Tietjen                          Executive Vice President, Treasurer              August 20, 1998
---------------------------                 and Chief Financial Officer
John W. Tietjen

                                            Vice Chairman of the Board and Director
/s/Joseph M. Adamko                                                                          August 20, 1998
---------------------------
Joseph M. Adamko


/s/Lillian Berkman                          Director                                         August 20, 1998
---------------------------
Lillian Berkman


/s/Walter Feldesman                         Director                                         August 20, 1998
---------------------------
Walter Feldesman


/s/Allan F. Hershfield                      Director                                         August 26, 1998
---------------------------
Allan F. Hershfield


/s/Henry J. Humphreys                       Director                                         August 20, 1998
---------------------------
Henry J. Humphreys


/s/Maxwell M. Rabb                          Director                                         August 20, 1998
---------------------------
Maxwell M. Rabb


/s/Eugene T. Rossides                       Director                                         August 20, 1998
---------------------------
Eugene T. Rossides


/s/William C. Warren                        Director                                         August 20, 1998
---------------------------
William C. Warren
</TABLE>
<PAGE>   6
                                INDEX TO EXHIBITS

Exhibit           Description

5        Opinion of Jerrold Gilbert, Esq. as to the validity of the shares to be
         issued.

23.1     Consent of KPMG Peat Marwick LLP.

23.2     Consent of Jerrold Gilbert, Esq. (contained in Exhibit 5).

24       Power of Attorney (reference is made to the signature page).
[{"type": "S-8", "sequence": "1", "description": "STERLING BANCORP", "secsgml_size_bytes": 11406}]
{"company-data": {"conformed-name": "STERLING BANCORP", "cik": "0000093451", "assigned-sic": "6021", "irs-number": "132565216", "state-of-incorporation": "NY", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-63665", "film-number": "98711347"}, "business-address": {"street1": "430 PARK AVE", "city": "NEW YORK", "state": "NY", "zip": "10022-3299", "phone": "2128268044"}, "mail-address": {"street1": "430 PARK AVE", "city": "NEW YORK", "state": "NY", "zip": "10022-3299"}, "former-company": [{"former-conformed-name": "STANDARD PRUDENTIAL CORP /NEW/", "date-changed": "19781210"}, {"former-conformed-name": "STANDARD PRUDENTIAL UNITED CORP", "date-changed": "19681125"}]}
1
   As filed with the Securities and Exchange Commission on September 18, 1998
                                                           Registration No. 333-

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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

                                STERLING BANCORP
             (Exact name of registrant as specified in its charter)

          NEW YORK                                             13-2565216
(State or other jurisdiction of                             (I.R.S. Employer
incorporation or organization)                            Identification Number)

                                 430 Park Avenue
                          New York, New York 10022-3505
                                 (212) 826-8000
                        (Address, including zip code, and
                     telephone number, including area code,
                         of principal executive offices)

                      STERLING BANCORP STOCK INCENTIVE PLAN
                            (Full title of the plan)

                              Jerrold Gilbert, Esq.
             Executive Vice President, General Counsel and Secretary
                                Sterling Bancorp
                                 430 Park Avenue
                          New York, New York 10022-3505
                                 (212) 826-8044
            (Name, address, including zip code, and telephone number,
                   including area code, of agent for service)

                                    Copies to
                             Michael J. Segal, Esq.
                      Paul Weiss Rifkind Wharton & Garrison
                           1285 Avenue of the Americas
                               New York, NY 10019
                                 (212) 373-3000

                         CALCULATION OF REGISTRATION FEE
-------------------------------------------------------- ------------------------ ----------------- ----------------- --------------
                  Title Of Securities                            Amount           Proposed Maximum      Proposed           Amount
                         To Be                                    To Be            Offering Price       Maximum              Of
                      Registered                               Registered          Per Share (1)       Aggregate        Registration
                                                                                                        Offering            Fee
                                                                                                         Price
-------------------------------------------------------- ------------------------ ----------------- ----------------- --------------
Common Stock $1.00 Par Value (including associated and           400,000              $20.875          $8,350,000        $2,463.25
attached rights to purchase shares of capital stock
under the Company's Shareholder Protection Rights
Agreement dated as of May 21, 1998.
======================================================== ======================== ================= ================= ==============
(1) Estimated solely for calculating the amount of the registration fee,
pursuant to Rule 457(h) under the Securities Act of 1933 (the "Securities Act")
based upon the average of the high and low sales prices of the Common Shares as
reported by the New York Stock Exchange on September 15, 1998.
2
                                     PART II

Item 3.  INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE

         The following documents, filed with the Securities and Exchange
Commission (the "Commission") by Sterling Bancorp, a New York corporation (the
"Company"), are incorporated herein by reference:

(a)      The Company's Annual Report on Form 10-K for the fiscal year ended
         December 31, 1997 (File No. 001-05273), filed pursuant to the
         Securities Exchange Act of 1934, as amended (the "Exchange Act");

(b)      The Company's Quarterly Reports on Form 10-Q for the quarters ended
         March 31, 1998 and June 30, 1998 (File No. 001-05273), filed pursuant
         to the Exchange Act;

(c)      The Company's Current Report on Form 8-K filed on June 5, 1998 (File
         No. 001-05273), pursuant to the Exchange Act;

(d)      The Company's Registration Statement on Form S-8 filed on May 20, 1997
         (File No. 333-27473), pursuant to the Securities Act; and

(e)      The description of the Company's Common Stock, $1.00 par value,
         contained in the Company's Registration Statement filed under the
         Exchange Act, including all amendments or reports filed for the purpose
         of updating such description, and the description of rights associated
         and attached to the Common Stock ("Rights") to purchase the Company's
         Series E Preferred Shares, $5.00 par value ("Preferred Shares"), or
         fractions thereof, at a Purchase Price of $100.00 per one one-hundredth
         of a Preferred Share, contained in the Company's Registration Statement
         therefor filed under the Exchange Act on June 15, 1998, including all
         amendments or reports filed for the purpose of updating such
         description.

         All documents subsequently filed by the Company with the Commission
pursuant to Sections 13(a), 13(c), 14 or 15(d) of the Exchange Act subsequent to
the date of this Registration Statement and prior to the filing of a
post-effective amendment which indicates that all securities offered hereby have
been sold or which deregisters all securities then remaining unsold shall be
deemed to be incorporated herein by reference and to be a part hereof from the
date of the filing of such documents with the Commission.
3
Item 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL

An opinion on the validity of the securities being registered hereunder has been
given by Jerrold Gilbert, Esq., General Counsel of the Company. Mr. Gilbert
holds options to purchase 42,000 Common Shares, with attached and associated
Rights, being registered hereunder.

Item 8.  EXHIBITS

5        Opinion of Jerrold Gilbert, Esq. as to the validity of the shares to be
         issued.

23.1     Consent of KPMG Peat Marwick LLP.

23.2     Consent of Jerrold Gilbert, Esq. (contained in Exhibit 5).

24       Power of Attorney (reference is made to the signature page).
4
                                   SIGNATURES

         Pursuant to the requirements of the Securities Act, the Company
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 New York, State of New York, on the 20th day of
August, 1998.

                                STERLING BANCORP

                                             By: /s/ Louis J. Cappelli
                                                     Louis J. Cappelli
                                                     Chairman of the Board and
                                                     Chief Executive Officer

         KNOW ALL MEN BY THESE PRESENTS, that each person whose signature
appears below constitutes and appoints Louis J. Cappelli, John C. Millman and
Jerrold Gilbert his true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities, to sign any and all amendments to this registration and
to file the same, with exhibits thereto, and other documents in connection
therewith with the Commission, granting unto said attorney-in-fact and agent
full power and authority to do and perform each and every act and thing
requisite and necessary to be done, as fully to all intents and purposes as he
might or could do in person, hereby ratifying and confirming all that said
attorney-in-fact and agent or any of them, or their or his substitute or
substitutes, may lawfully do or cause to be done by virtue hereof.

         Pursuant to the requirements of the Securities Act, this registration
statement has been duly signed by the following persons in the capacities and on
the dates indicated.
Signature                                    Title                                Date
                ---------                                    -----                                ----
/s/Louis J. Cappelli                        Chairman of the Board,                           August 20, 1998
---------------------------                 Chief Executive Officer
Louis J. Cappelli                           and Director

/s/John C. Millman                          President and Director                           August 20, 1998
------------------
John C. Millman
5
/s/John W. Tietjen                          Executive Vice President, Treasurer              August 20, 1998
---------------------------                 and Chief Financial Officer
John W. Tietjen

                                            Vice Chairman of the Board and Director
/s/Joseph M. Adamko                                                                          August 20, 1998
---------------------------
Joseph M. Adamko

/s/Lillian Berkman                          Director                                         August 20, 1998
---------------------------
Lillian Berkman

/s/Walter Feldesman                         Director                                         August 20, 1998
---------------------------
Walter Feldesman

/s/Allan F. Hershfield                      Director                                         August 26, 1998
---------------------------
Allan F. Hershfield

/s/Henry J. Humphreys                       Director                                         August 20, 1998
---------------------------
Henry J. Humphreys

/s/Maxwell M. Rabb                          Director                                         August 20, 1998
---------------------------
Maxwell M. Rabb

/s/Eugene T. Rossides                       Director                                         August 20, 1998
---------------------------
Eugene T. Rossides

/s/William C. Warren                        Director                                         August 20, 1998
---------------------------
William C. Warren
6
                                INDEX TO EXHIBITS

Exhibit           Description

5        Opinion of Jerrold Gilbert, Esq. as to the validity of the shares to be
         issued.

23.1     Consent of KPMG Peat Marwick LLP.

23.2     Consent of Jerrold Gilbert, Esq. (contained in Exhibit 5).

24       Power of Attorney (reference is made to the signature page).