Exhibit 99.3

GREATER BAY BANCORP

Offer to Exchange Its

5.25% Senior Notes, Series B, Due March 31, 2008,

Which Have Been Registered Under the Securities Act (the “Exchange Notes”)

For

5.25% Senior Notes, Series A, Due March 31, 2008 (the “Original Notes”)

To: Brokers, Dealers, Commercial Banks,

Trust Companies and Other Nominees:

Greater Bay Bancorp (“Greater Bay”) is offering, upon and subject to the terms and conditions set forth in a prospectus dated             , 2003 (as the same may be amended or supplemented from time to time, the “Prospectus”), and the enclosed letter of transmittal (the “Letter of Transmittal”), to exchange (the “Exchange Offer”) its 5.25% Exchange Notes for any and all of its outstanding 5.25% Original Notes. The Exchange Offer is being made in order to satisfy certain obligations of Greater Bay contained in the Registration Rights Agreement, dated March 24, 2003, among Greater Bay and Keefe, Bruyette & Woods, Inc., Sandler O’Neill & Partners, L.P., and FTN Financial Securities Corp.

We are requesting that you contact your clients for whom you hold Original Notes regarding the Exchange Offer. For your information and for forwarding to your clients for whom you hold Original Notes registered in your name or in the name of your nominee, or who hold Original Notes registered in their own names, we are enclosing the following documents:

1. The Prospectus dated             , 2003;

2. The Letter of Transmittal for your use and for the information (or the use, where relevant) of your clients;

3. A Notice of Guaranteed Delivery to be used to accept the Exchange Offer if certificates for Original Notes are not immediately available or time will not permit all required documents to reach the Exchange Agent prior to the Expiration Date (as defined below) or if the procedure for book-entry transfer cannot be completed on a timely basis;

4. A form of letter which may be sent to your clients for whose account you hold Original Notes registered in your name or the name of your nominee, with space provided for obtaining such clients’ instructions with regard to the Exchange Offer; and

5. Guidelines for Certification of Taxpayer Identification Number on Substitute Form W-9.

Your prompt action is requested. The Exchange Offer will expire at 5:00 p.m., Eastern time, on             , 2003, or on such later date or time to which Greater Bay may extend the Exchange Offer (the “Expiration Date”). The Original Notes tendered pursuant to the Exchange Offer may be withdrawn at any time before the Expiration Date.

To participate in the Exchange Offer, a duly executed and properly completed Letter of Transmittal (or facsimile of the letter), with any required signature guarantees and any other required documents, should be sent to the Exchange Agent and certificates representing the Original Notes should be delivered to the Exchange Agent, all in accordance with the instructions set forth in the Letter of Transmittal and the Prospectus.

If holders of Original Notes wish to tender, but it is impracticable for them to forward their certificates for Original Notes before the expiration of the Exchange Offer or to comply with the book-entry transfer procedures on a timely basis, a tender may be effected by following the guaranteed delivery procedures described in the Prospectus under “The Exchange Offer—Procedures for Tendering Original Notes—Guaranteed Delivery.”

Greater Bay will, upon request, reimburse brokers, dealers, commercial banks and trust companies for reasonable and necessary costs and expenses incurred by them in forwarding the Prospectus and the related documents to the beneficial owners of Original Notes held by them as nominee or in a fiduciary capacity. Greater Bay will pay or cause to be paid all stock transfer taxes applicable to the exchange of Original Notes pursuant to the Exchange Offer, except as set forth in Instruction 13 of the Letter of Transmittal.

Any inquiries you may have with respect to the Exchange Offer, or requests for additional copies of the enclosed materials, should be directed to Wilmington Trust Company, the Exchange Agent for the Original Notes, at its address and telephone number set forth on the front of the Letter of Transmittal.

Very truly yours,

GREATER BAY BANCORP

Nothing herein or in the enclosed documents shall constitute you or any person as an agent of the trust or the Exchange Agent, or authorize you or any other person to use any document or make any statements on behalf of either of them with respect to the Exchange Offer, except for statements expressly made in the Prospectus or the Letter of Transmittal.

Enclosures

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