<PAGE>   1
                                                   Registration No. ____________
================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM S-8
                             REGISTRATION STATEMENT

                        UNDER THE SECURITIES ACT OF 1933

                           GENOVESE DRUG STORES, INC.
             (Exact name of registrant as specified in its charter)

            Delaware                                           11-1556812
(State or other jurisdiction of                            (I.R.S. Employer
incorporation or organization)                             Identification No.)

                                 80 Marcus Drive
                            Melville, New York 11747
           (Address of principal executive offices including zip code)

              GENOVESE DRUG STORES, INC. 1984 EMPLOYEE STOCK OPTION
                       AND STOCK APPRECIATION RIGHTS PLAN
                            (Full title of the plan)

                                 GENE L. WEXLER
                       Vice President and General Counsel
                           Genovese Drug Stores, Inc.
                                 80 Marcus Drive
                            Melville, New York 11747
                     (Name and address of agent for service)

                                 (516) 845-8433
          (Telephone number, including area code, of agent for service)

                         CALCULATION OF REGISTRATION FEE
<TABLE>
<CAPTION>
=======================================================================================
                                         Proposed          Proposed
    Title of                              maximum           maximum
   securities            Amount          offering          aggregate        Amount of
     to be               to be           price per         offering        registration
   registered         registered           share             price             fee
=======================================================================================
<S>                  <C>                 <C>            <C>                <C>
 Class A Common
Stock, par value
$1.00 per share      800,000 shares(1)   $8.9375(2)     $7,150,000.00(2)      $2466.00
=======================================================================================
</TABLE>

(1)    Such additional indeterminable number of shares of Class A Common Stock
       is hereby registered as may be required by reason of the anti-dilution
       provisions of the Genovese Drug Stores, Inc. 1984 Employee Stock Option
       and Stock Appreciation Rights Plan.

(2)    Pursuant to Rule 457(h) under the Securities Act of 1933, this estimate
       is made solely for the purpose of calculating the amount of the
       registration fee and is based on the average of the high and low prices
       of the Class A Common Stock on the American Stock Exchange on June 14,
       1996.
<PAGE>   2

                                     PART II

ITEM 3.     INCORPORATION OF DOCUMENTS BY REFERENCE.

            The following documents heretofore filed by Genovese Drug Stores,
Inc. (the "Company") with the Securities and Exchange Commission are
incorporated herein by reference:

            (1)   Annual Report of the Company on Form 10-K for the fiscal year
                  ended February 2, 1996;

            (2)   The description of the Company's Class A Common Stock, par
                  value $1.00 per share, contained in the Company's Registration
                  Statement filed pursuant to Section 12 of the Securities
                  Exchange Act of 1934 and any amendments and reports filed for
                  the purpose of updating that description; and

            (3)   Form S-8 Registration Statement under the Securities Act of
                  1933, as amended, filed with the Commission on August 2, 1994
                  (Registration No. 33-54857).

            All documents that shall be filed by the Company pursuant to
Sections 13(a), 13(c), 14 and 15(d) of the Securities Exchange Act of 1934
subsequent to the filing of this registration statement and prior to the filing
of a post-effective amendment indicating that all securities offered under the
Genovese Drug Stores, Inc. 1984 Employee Stock Option and Stock Appreciation
Rights Plan (the "Plan") have been sold or deregistering all securities then
remaining unsold thereunder shall be deemed to be incorporated herein by
reference and shall be deemed to be a part hereof from the date of filing
thereof.

ITEM 5.     INTERESTS OF NAMED EXPERTS AND COUNSEL.

            As of the date of filing of this registration statement, Gene L.
Wexler, Vice President and General Counsel of the Company, who is opining as to
the validity of the securities being registered herewith, beneficially owned
19,561 shares of the Company's Class A Common Stock.

ITEM 8.     EXHIBITS.

            4(a)  Genovese Drug Stores, Inc. 1984 Employee Stock Option and
                  Stock Appreciation Rights Plan, as amended

            5     Opinion of Counsel

            23(a) Consent of Independent Auditors

              (b) Consent of Counsel (included in Exhibit 5)

            24    Powers of Attorney


                                      II-1
<PAGE>   3
                                   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 THIS REGISTRATION STATEMENT 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 MELVILLE, STATE OF NEW
YORK, ON THIS 17TH DAY OF JUNE, 1996.

                                              GENOVESE DRUG STORES, INC.


                                              By: /s/ Leonard Genovese
                                                  -----------------------------
                                                  Chairman of the Board
                                                  and President




                                      II-2
<PAGE>   4
            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>
*Leonard Genovese            Chairman of the Board,         June 17, 1996
 -----------------------     President and Director
 Leonard Genovese            (Principal Executive
                             Officer)

*Herbert J. Kett             Vice Chairman                  June 17, 1996
 -----------------------     and Director
 Herbert J. Kett             

*Allan Patrick               Executive Vice President       June 17, 1996
 -----------------------     and Director
 Allan Patrick               

*Jerome Stengel              Vice President and             June 17, 1996
 -----------------------     Treasurer (Principal
 Jerome Stengel              Financial and
                             Accounting Officer)

*Frances Genovese Wangberg        Director                  June 17, 1996
 -------------------------
 Frances Genovese Wangberg

*William J. McKenna               Director                  June 17, 1996
 -----------------------
 William J. McKenna

*Charles Hayward                  Director                  June 17, 1996
 -----------------------
 Charles Hayward

*Abraham Allen                    Director                  June 17, 1996
 -----------------------
 Abraham Allen

*Thomas M. Cooney                 Director                  June 17, 1996
 -----------------------
 Thomas M. Cooney

*Thomas J. Moran                  Director                  June 17, 1996
 -----------------------
 Thomas J. Moran
</TABLE>



                                      II-3
<PAGE>   5

*     This registration statement has been signed on behalf of the above-named
      directors and officers of the Company by Leonard Genovese, Chairman of the
      Board and President of the Company, as attorney-in-fact pursuant to powers
      of attorney filed with the Securities and Exchange Commission as Exhibit
      24 to this registration statement.

DATED:  June 17, 1996                       By: /s/ Leonard Genovese
                                                --------------------
                                               Attorney-in-Fact




                                      II-4
<PAGE>   6
                                  EXHIBIT INDEX

<TABLE>
<CAPTION>
                                                                       Page Number
Exhibit                                                              in Sequentially
Number                     Exhibit Description                        Numbered Copy
- -------                    -------------------                       ---------------
<S>            <C>                                                   <C>
4(a)           Genovese Drug Stores, Inc. 1984 Employee Stock
               Option and Stock Appreciation Rights Plan, as
               amended

5              Opinion of Counsel

23(a)          Consent of Independent Auditors

23(b)          Consent of Counsel (included in Exhibit 5)

24             Powers of Attorney
</TABLE>




                                      II-5
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1
                                                   Registration No. ____________
================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM S-8
                             REGISTRATION STATEMENT

                        UNDER THE SECURITIES ACT OF 1933

                           GENOVESE DRUG STORES, INC.
             (Exact name of registrant as specified in its charter)

            Delaware                                           11-1556812
(State or other jurisdiction of                            (I.R.S. Employer
incorporation or organization)                             Identification No.)

                                 80 Marcus Drive
                            Melville, New York 11747
           (Address of principal executive offices including zip code)

              GENOVESE DRUG STORES, INC. 1984 EMPLOYEE STOCK OPTION
                       AND STOCK APPRECIATION RIGHTS PLAN
                            (Full title of the plan)

                                 GENE L. WEXLER
                       Vice President and General Counsel
                           Genovese Drug Stores, Inc.
                                 80 Marcus Drive
                            Melville, New York 11747
                     (Name and address of agent for service)

                                 (516) 845-8433
          (Telephone number, including area code, of agent for service)

                         CALCULATION OF REGISTRATION FEE
=======================================================================================
                                         Proposed          Proposed
    Title of                              maximum           maximum
   securities            Amount          offering          aggregate        Amount of
     to be               to be           price per         offering        registration
   registered         registered           share             price             fee
=======================================================================================
Class A Common
Stock, par value
$1.00 per share      800,000 shares(1)   $8.9375(2)     $7,150,000.00(2)      $2466.00
=======================================================================================
(1)    Such additional indeterminable number of shares of Class A Common Stock
       is hereby registered as may be required by reason of the anti-dilution
       provisions of the Genovese Drug Stores, Inc. 1984 Employee Stock Option
       and Stock Appreciation Rights Plan.

(2)    Pursuant to Rule 457(h) under the Securities Act of 1933, this estimate
       is made solely for the purpose of calculating the amount of the
       registration fee and is based on the average of the high and low prices
       of the Class A Common Stock on the American Stock Exchange on June 14,
       1996.
2

                                     PART II

ITEM 3.     INCORPORATION OF DOCUMENTS BY REFERENCE.

            The following documents heretofore filed by Genovese Drug Stores,
Inc. (the "Company") with the Securities and Exchange Commission are
incorporated herein by reference:

            (1)   Annual Report of the Company on Form 10-K for the fiscal year
                  ended February 2, 1996;

            (2)   The description of the Company's Class A Common Stock, par
                  value $1.00 per share, contained in the Company's Registration
                  Statement filed pursuant to Section 12 of the Securities
                  Exchange Act of 1934 and any amendments and reports filed for
                  the purpose of updating that description; and

            (3)   Form S-8 Registration Statement under the Securities Act of
                  1933, as amended, filed with the Commission on August 2, 1994
                  (Registration No. 33-54857).

            All documents that shall be filed by the Company pursuant to
Sections 13(a), 13(c), 14 and 15(d) of the Securities Exchange Act of 1934
subsequent to the filing of this registration statement and prior to the filing
of a post-effective amendment indicating that all securities offered under the
Genovese Drug Stores, Inc. 1984 Employee Stock Option and Stock Appreciation
Rights Plan (the "Plan") have been sold or deregistering all securities then
remaining unsold thereunder shall be deemed to be incorporated herein by
reference and shall be deemed to be a part hereof from the date of filing
thereof.

ITEM 5.     INTERESTS OF NAMED EXPERTS AND COUNSEL.

            As of the date of filing of this registration statement, Gene L.
Wexler, Vice President and General Counsel of the Company, who is opining as to
the validity of the securities being registered herewith, beneficially owned
19,561 shares of the Company's Class A Common Stock.

ITEM 8.     EXHIBITS.

            4(a)  Genovese Drug Stores, Inc. 1984 Employee Stock Option and
                  Stock Appreciation Rights Plan, as amended

            5     Opinion of Counsel

            23(a) Consent of Independent Auditors

              (b) Consent of Counsel (included in Exhibit 5)

            24    Powers of Attorney

                                      II-1
3
                                   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 THIS REGISTRATION STATEMENT 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 MELVILLE, STATE OF NEW
YORK, ON THIS 17TH DAY OF JUNE, 1996.

                                              GENOVESE DRUG STORES, INC.

                                              By: /s/ Leonard Genovese
                                                  -----------------------------
                                                  Chairman of the Board
                                                  and President

                                      II-2
4
            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
      ---------                      -----                     ----
*Leonard Genovese            Chairman of the Board,         June 17, 1996
 -----------------------     President and Director
 Leonard Genovese            (Principal Executive
                             Officer)

*Herbert J. Kett             Vice Chairman                  June 17, 1996
 -----------------------     and Director
 Herbert J. Kett             

*Allan Patrick               Executive Vice President       June 17, 1996
 -----------------------     and Director
 Allan Patrick               

*Jerome Stengel              Vice President and             June 17, 1996
 -----------------------     Treasurer (Principal
 Jerome Stengel              Financial and
                             Accounting Officer)

*Frances Genovese Wangberg        Director                  June 17, 1996
 -------------------------
 Frances Genovese Wangberg

*William J. McKenna               Director                  June 17, 1996
 -----------------------
 William J. McKenna

*Charles Hayward                  Director                  June 17, 1996
 -----------------------
 Charles Hayward

*Abraham Allen                    Director                  June 17, 1996
 -----------------------
 Abraham Allen

*Thomas M. Cooney                 Director                  June 17, 1996
 -----------------------
 Thomas M. Cooney

*Thomas J. Moran                  Director                  June 17, 1996
 -----------------------
 Thomas J. Moran
II-3
5

*     This registration statement has been signed on behalf of the above-named
      directors and officers of the Company by Leonard Genovese, Chairman of the
      Board and President of the Company, as attorney-in-fact pursuant to powers
      of attorney filed with the Securities and Exchange Commission as Exhibit
      24 to this registration statement.

DATED:  June 17, 1996                       By: /s/ Leonard Genovese
                                                --------------------
                                               Attorney-in-Fact

                                      II-4
6
                                  EXHIBIT INDEX
Page Number
Exhibit                                                              in Sequentially
Number                     Exhibit Description                        Numbered Copy
- -------                    -------------------                       ---------------
4(a)           Genovese Drug Stores, Inc. 1984 Employee Stock
               Option and Stock Appreciation Rights Plan, as
               amended

5              Opinion of Counsel

23(a)          Consent of Independent Auditors

23(b)          Consent of Counsel (included in Exhibit 5)

24             Powers of Attorney
II-5