EXHIBIT 99.4

OFFER TO EXCHANGE
EACH OUTSTANDING SHARE
OF
AGA MEDICAL HOLDINGS, INC. COMMON STOCK FOR
$20.80 IN CASH OR $20.80 IN FAIR MARKET VALUE
OF ST. JUDE MEDICAL, INC. COMMON STOCK
SUBJECT TO ADJUSTMENT AND PRORATION
PURSUANT TO THE EXCHANGE OFFER
DESCRIBED IN THE PROSPECTUS/OFFER TO EXCHANGE, DATED OCTOBER 20, 2010
THE EXCHANGE OFFER AND THE WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT
(ONE MINUTE AFTER 11:59 P.M.) NEW YORK TIME,
ON NOVEMBER 17, 2010, UNLESS EXTENDED.

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

        This letter relates to the offer by Asteroid Subsidiary Corporation ("Asteroid"), a Delaware corporation and an indirect wholly owned subsidiary of St. Jude Medical, Inc., a Minnesota corporation ("St. Jude Medical"), to acquire all of the outstanding shares of common stock of AGA Medical Holdings, Inc. ("AGA"), par value $0.01 per share ("AGA common stock"), by means of an exchange offer (the "Offer") and a subsequent merger of Asteroid into AGA. The Offer is being made in connection with an agreement and plan of merger and reorganization, dated as of October 15, 2010, by and among St. Jude Medical, Asteroid and AGA. Pursuant to the terms of the Offer described in the prospectus/offer to exchange, dated October 20, 2010 (as the same may, from time to time, be amended, supplemented or finalized, the "prospectus/offer to exchange"), and in the related Letter of Election and Transmittal enclosed herewith, each share of AGA common stock validly tendered and not properly withdrawn shall be exchanged at the election of the holder for either:

•

$20.80 in cash, without interest, or

•

a fraction of a share or number of shares (the "Exchange Rate") of St. Jude Medical common stock, par value $0.10 per share ("St. Jude Medical common stock"), equal to $20.80 divided by the volume weighted average of the daily closing prices per share of St. Jude Medical common stock on the New York Stock Exchange for the ten trading days ending on and including the second trading day preceding the expiration date of the Offer, as it may be extended (the "Expiration Date"),

        subject to the terms and conditions described in the prospectus/offer to exchange and the Letter of Election and Transmittal. Holders of AGA common stock may elect cash for some shares and shares of St. Jude Medical common stock for others.

        The aggregate amount of cash and number of shares of St. Jude Medical common stock that a stockholder may receive in the Offer are subject to the following limits:

•

the amount of cash payable in the Offer is $20.80 multiplied by 50% of the aggregate number of shares of AGA common stock tendered in the Offer. Thus, except as described below, 50% of the shares of AGA common stock tendered in the Offer will be exchanged for cash;

•

the number of shares of St. Jude Medical common stock issuable in the Offer is the Exchange Rate multiplied by 50% of the aggregate number of shares of AGA common stock tendered in the Offer. Thus, except as described below, subject to the other limitations described herein, 50% of the shares of AGA common stock tendered in the Offer will be exchanged for shares of St. Jude Medical common stock;

•

in no event will the number of shares of St. Jude Medical common stock to be issued in the Offer and the Merger exceed 19.9% of shares of St. Jude Medical common stock outstanding on the date on which shares of AGA common stock are first accepted for payment under the Offer; and

•

elections will be subject to adjustment and proration if tendering holders of shares of AGA common stock, in the aggregate, elect to receive more than the maximum amount of consideration to be paid as cash or shares of St. Jude Medical common stock.

        Please furnish copies of the enclosed materials to those of your clients for whose accounts you hold shares of AGA common stock registered in your name or in the name of your nominee.

        The Offer is subject to several conditions, including: (a) St. Jude Medical having received a number of validly tendered shares of AGA common stock that, together with the shares owned by St. Jude Medical or any of its subsidiaries, would represent at least a majority of the outstanding shares of AGA common stock on a fully diluted basis on the date of purchase; (b) all applicable waiting periods under the Hart-Scott-Rodino Act and any non-U.S. antitrust, competition or similar notification or clearance law having expired or terminated; and (c) the shares of St. Jude Medical common stock to be issued in the Offer having been approved for listing on the NYSE and the registration statement of which the prospectus/offer to exchange is a part having been declared effective by the SEC and not be the subject of any stop order or proceedings seeking a stop order. The Offer is also subject to the other conditions described in the prospectus/offer to exchange in the section entitled "The Merger Agreement—Conditions to the Offer," which you should review in detail.

        For your information and for forwarding to your clients for whom you hold shares of AGA common stock registered in your name or in the name of your nominee, we are enclosing the following documents:

1.

The prospectus/offer to exchange dated October 20, 2010.



2.

The Letter of Election and Transmittal for your use in accepting the Offer and tendering shares of AGA common stock and for the information of your clients. Facsimile copies of the Letter of Election and Transmittal with manual signatures may be used to tender shares of AGA common stock.



3.

The Notice of Guaranteed Delivery to be used to accept the Offer if certificates evidencing shares of AGA common stock are not immediately available or if such certificates and all other required documents cannot be delivered to Wells Fargo Shareowner Services (the "Exchange Agent") on or prior to the expiration date (as defined in the Letter of Election and Transmittal) or if the procedures for book-entry transfer cannot be completed by the expiration date.



4.

A printed form of letter which may be sent to your clients for whose accounts you hold shares of AGA common stock registered in your name or in the name of your nominee, with space provided for obtaining such clients' instructions with regard to the Offer.



5.

Guidelines for certification of Taxpayer Identification Number on Substitute Form W-9. Stockholders who fail to complete and sign the Substitute Form W-9, or such other IRS form as may be required, may be subject to a required federal backup withholding tax of up to 31% of any cash payable to such stockholder or other payee pursuant to the Offer.



6.

A copy of AGA's Solicitation/Recommendation Statement on Schedule 14D-9.



7.

A return envelope addressed to the Exchange Agent for your use only.

        Upon the terms and subject to the conditions of the Offer (including, if the Offer is extended or amended, the terms and conditions of any such extension or amendment), Asteroid will accept for exchange shares of AGA common stock which are validly tendered prior to the expiration date and not theretofore withdrawn when and if Asteroid gives oral or written notice to the Exchange Agent of Asteroid's acceptance of such shares of AGA common stock for exchange pursuant to the Offer. Issuance of shares of St. Jude Medical common stock and payment of cash payable pursuant to the Offer, as applicable, will in all cases be made only after timely receipt by the Exchange Agent of (i) certificates for such shares of AGA common stock, or timely confirmation of a book-entry transfer of such shares of AGA common stock into the Exchange Agent's account at the Depository Trust

Company, pursuant to the procedures described in the section of the prospectus/offer to exchange entitled "The Transaction—Procedure for Tendering," (ii) a properly completed and duly executed Letter of Election and Transmittal (or a properly completed and manually signed facsimile thereof) or an Agent's Message (as defined in the prospectus/offer to exchange) in connection with a book-entry transfer and (iii) all other documents required by the Letter of Election and Transmittal.

        Neither St. Jude Medical nor Asteroid nor any officer, director, shareholder, agent or other representative of St. Jude Medical or Asteroid will pay any fees or commissions to any broker or dealer or other person (other than Georgeson Inc. (the "Information Agent") and the Exchange Agent) with respect to soliciting tenders of shares of AGA common stock pursuant to the Offer. Asteroid will, however, upon request, reimburse brokers, dealers, commercial banks and trust companies for customary mailing and handling costs incurred by them in forwarding the enclosed materials to their customers.

We urge you to contact your clients as promptly as possible. Please note that the Offer and withdrawal rights will expire at 12:00 midnight (one minute after 11:59 P.M.) New York time, on the evening of November 17, 2010, unless the Offer is extended. Any shares of AGA common stock tendered pursuant to the Offer may be withdrawn at any time before the Expiration Date, by strictly complying with the procedures described in the section of the prospectus/offer to exchange entitled "The Transaction—Withdrawal Rights" and the Letter of Election and Transmittal.

        In order to take advantage of the Offer, a duly executed and properly completed Letter of Election and Transmittal (or a manually signed facsimile thereof), with any required signature guarantees, or an Agent's Message in connection with a book-entry transfer of shares of AGA common stock, and any other required documents, should be sent to the Exchange Agent, and certificates representing the tendered shares of AGA common stock should be delivered or such shares of AGA common stock should be tendered by book-entry transfer, all in accordance with the Instructions described in the Letter of Election and Transmittal and in the prospectus/offer to exchange.

        If holders of shares of AGA common stock wish to tender, but it is impracticable for them to forward their certificates or other required documents or to complete the procedures for delivery by book-entry transfer prior to the expiration of the Offer, a tender may be effected by following the guaranteed delivery procedures specified in the section of the prospectus/offer to exchange entitled "The Transaction—Procedure for Tendering."

        Any inquiries you may have with respect to the Offer should be addressed to, and additional copies of the enclosed materials may be obtained from us, at the address and telephone number set forth on the back cover of the prospectus/offer to exchange.

Very truly yours,

Georgeson Inc.

Nothing contained herein or in the enclosed documents shall authorize you to be the agent of St. Jude Medical, Asteroid, the Information Agent, the Exchange Agent or any affiliate of any of the foregoing, or authorize you or any other person to use any document or make any statement on behalf of any of them in connection with the Offer other than the documents enclosed herewith and the statements contained therein.