Exhibit 99.3

EASTERN VIRGINIA BANKSHARES, INC.

P.O. Box 1455

330 Hospital Road

Tappahannock, Virginia 22560

LETTER TO NOMINEE HOLDERS

WHOSE CLIENTS ARE BENEFICIAL HOLDERS

EASTERN VIRGINIA BANKSHARES, INC.

1,098,901 Shares of Common Stock

Offered Pursuant to Rights Distributed to Record Shareholders of

Eastern Virginia Bankshares, Inc.

To Brokers, Dealers, Custodian Banks, and Other Nominee Holders:

This letter is being distributed to brokers, dealers, custodian banks and other nominee holders in connection with the rights offering (the “Rights Offering”) by Eastern Virginia Bankshares, Inc. (the “Company”) of shares of its Common Stock, par value $2.00 per share (the “Common Stock”), pursuant to non-transferable subscription rights (the “Rights”) distributed to all holders of record (“Record Holders”) of shares of Common Stock, at 5:00 pm, Eastern time, on May 3, 2013 (the “Record Date”). The Rights are described in the Company’s Prospectus, dated May [            ], 2013 (the “Prospectus”).

In the Rights Offering, the Company is offering an aggregate of 1,098,901 shares of its Common Stock (the “Underlying Shares”) pursuant to the Prospectus. The Rights will expire, if not exercised, at 5:00 p.m., Eastern Time, on Friday, June 14, 2013, unless extended by the Board of Directors of the Company (as it may be extended, the “Expiration Date”).

As described in the accompanying Prospectus, each Record Holder will receive one Right for every share of Common Stock owned of record as of 5:00 p.m., Eastern time, on the Record Date.

Each Right allows the holder thereof to subscribe for 0.181051448 of a share of Common Stock (the “Basic Subscription Right”) at the cash price of $4.55 per whole share (the “Subscription Price”), subject to the Company’s right to limit the beneficial ownership of any individual shareholder to no more than 4.9% (unless such shareholder’s beneficial ownership exceeded 4.9% on the Record Date for the Rights Offering) (the “4.9% Rights Offering Restriction”). Fractional shares or cash in lieu of fractional shares will not be issued in the Rights Offering. Instead, fractional shares resulting from the exercise of the Basic Subscription Right will be eliminated by rounding down to the nearest whole share. As an example, if you owned 1,000 shares of Common Stock as of the Record Date, you would receive 1,000 Rights pursuant to your Basic Subscription Right that would entitle you to purchase 181 shares of common stock (181.051448 rounded down to the nearest whole share) at the Subscription Price of $4.55 per whole share, subject to the 4.9% Rights Offering Restriction.

A holder of Rights may exercise all or a portion of the Basic Subscription Right, subject to the 4.9% Rights Offering Restriction, or may choose not to exercise any of the Basic Subscription Right. However, if a holder of Rights does not fully exercise the Basic Subscription Right, such holder will not be entitled to purchase Excess Shares (as defined below) under the Over-subscription Privilege (as defined below).

In addition to the Basic Subscription Right, each holder of Rights who exercises his Basic Subscription Right in full will be eligible, subject to the 4.9% Rights Offering Restriction, to subscribe (the “Over-subscription Privilege”) at the same Subscription Price of $4.55 per whole share for additional shares of Common Stock if any Underlying Shares are not purchased by other holders of Rights under their Basic Subscription Rights as of the Expiration Date (the “Excess Shares”). Each holder of Rights may exercise his Over-subscription Privilege only if

he exercised his Basic Subscription Right in full and other holders of Rights do not exercise their Basic Subscription Rights in full. If there is not a sufficient number of Excess Shares to satisfy all requests for subscriptions made under the Over-subscription Privilege, the Company will allocate the remaining Excess Shares pro rata, after eliminating all fractional shares, among those Rights holders who exercised their Over-subscription Privileges in proportion to the number of shares of Common Stock owned by such Right holder on the Record Date, relative to the number of shares of Common Stock owned on the Record Date by all Right holders exercising their Over-subscription Privilege, subject to the 4.9% Rights Offering Restriction. If this pro rata allocation results in any person receiving a greater number of Excess Shares than the person subscribed for pursuant to the exercise of the Over-subscription Privilege, then such person will be allocated only that number of Excess Shares for which the person over-subscribed, subject to the 4.9% Rights Offering Restriction, and the remaining Excess Shares will be re-allocated among all other persons exercising the Over-subscription Privilege on the same pro rata basis described above. The proration process will be repeated until all Excess Shares have been allocated.

For the purposes of determining their eligibility for the Over-subscription Privilege, holders will be deemed to have exercised their Rights under the Basic Subscription Right in full if they subscribe for the maximum number of whole Underlying Shares available under their Basic Subscription Right. See “The Rights Offering—The Subscription Rights” in the Prospectus.

The Rights are evidenced by a Rights certificate (a “Subscription Rights Certificate”) registered in your name or the name of your nominee. Each beneficial owner of shares of Common Stock registered in your name or the name of your nominee is entitled to one Right for every share of Common Stock owned by such beneficial owner as of the Record Date. The back of the Subscription Rights Certificate contains the exercise form for participating in the Rights Offering. If not exercised, your Subscription Rights Certificate will cease to have any value when the Rights Offering expires.

We are asking persons who hold shares of Common Stock beneficially and who have received the Rights distributable with respect to those shares through a broker, dealer, custodian bank or other nominee holder, as well as persons who hold certificates of Common Stock directly and prefer to have such institutions effect transactions relating to the Rights on their behalf, to contact the appropriate institution or nominee and request it to effect the transactions for them. In addition, we are asking beneficial owners who wish to obtain a separate Subscription Rights Certificate to contact the appropriate nominee as soon as possible and request that a separate Subscription Rights Certificate be issued.

Please take prompt action to notify any beneficial owners of Common Stock as to the Rights Offering and the procedures and deadlines that must be followed to exercise their Rights. If you exercise the Over-subscription Privilege on behalf of beneficial owners of Rights, you will be required to certify to Registrar and Transfer Company (the “Subscription Agent”) and the Company, in connection with the exercise of the Over-subscription Privilege, as to the aggregate number of Rights that have been exercised pursuant to the Basic Subscription Privilege, whether the Basic Subscription Privilege of each beneficial owner of Rights on whose behalf you are acting has been exercised in full and the number of shares of Common Stock being subscribed for pursuant to the Over-subscription Privilege by each beneficial owner of Rights on whose behalf you are acting.

All commissions, fees and other expenses (including brokerage commissions and fees and transfer taxes), other than certain fees and expenses of the Subscription Agent and the Information Agent, incurred in connection with the exercise of the Rights will be for the account of the holder of the Rights, and none of such commissions, fees or expenses will be paid by the Company, the Subscription Agent, or the Information Agent.

Enclosed are copies of the following documents:

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Your prompt action is requested. To exercise the Rights, you must deliver the properly completed and signed Subscription Rights Certificate, together with the Nominee Holder Certification and payment in full of the total subscription amount that is required for all of the shares subscribed for in the Rights Offering, to the Subscription Agent as described further in the Prospectus. Do not send the Subscription Rights Certificate, Nominee Holder Certification or payment to the Company. The properly completed and executed Subscription Rights Certificate and Nominee Holder Certification, accompanied by full payment of the total subscription amount, must be received by the Subscription Agent, and your payment must clear, by no later than 5:00 p.m., Eastern time, on the Expiration Date. Failure to return the properly completed Subscription Rights Certificate and Nominee Holder Certification with the correct payment will result in your not being able to exercise the Rights held in your name on behalf of yourself or other beneficial owners. A Rights holder cannot cancel, revoke or otherwise amend the exercise of Rights (unless we are required by law to permit revocation). Rights not exercised before 5:00 p.m., Eastern time, on the Expiration Date will expire without value and you will have no further rights under them.

Additional copies of the enclosed materials may be obtained from our information agent, Eagle Rock Proxy Advisors, LLC, by calling (888) 669-2032 toll-free. You may also contact our information agent if you have any questions about the Rights Offering or require any assistance in exercising the Rights.

NOTHING IN THE PROSPECTUS OR IN THE ENCLOSED DOCUMENTS SHALL CONSTITUTE YOU OR ANY PERSON AS AN AGENT OF EASTERN VIRGINIA BANKSHARES, INC., THE SUBSCRIPTION AGENT, THE INFORMATION AGENT, OR ANY OTHER PERSON MAKING OR DEEMED TO BE MAKING OFFERS OF THE SECURITIES ISSUABLE UPON VALID EXERCISE OF THE RIGHTS, OR AUTHORIZE YOU OR ANY OTHER PERSON TO MAKE ANY STATEMENTS ON BEHALF OF ANY OF THEM WITH RESPECT TO THE OFFERING EXCEPT FOR STATEMENTS EXPRESSLY MADE IN THE PROSPECTUS.

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