Exhibit 24

LIMITED POWER OF ATTORNEY FOR

SEC REPORTING PURPOSES

Know all by these presents, that the undersigned hereby makes, constitutes, and appoints each of Jessica L. Mayer, James E. Barnett, Laura C. Dhaliwal, Amanda Pashi, Julie Gilbert, and any duly appointed Corporate Secretary of Cardinal Health, Inc. (the “Company”), with full power of substitution and re-substitution, acting individually, as the undersigned’s true and lawful attorney-in-fact, with full power and authority as hereinafter described on behalf of and in the name, place, and stead of the undersigned to:

(1)obtain credentials (including codes or passwords) to enable the undersigned to submit and file documents, forms, and information required by Section 16(a) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), or any rule or regulation of the U.S. Securities and Exchange Commission (“SEC”) via the Electronic Data Gathering and Retrieval (“EDGAR”) system, including: (i) preparing, executing in the undersigned’s name and on the undersigned’s behalf, and submitting to the SEC a Form ID (and any amendments thereto) or any other documents necessary or appropriate to obtain such credentials and legally binding the undersigned for purpose of the Form ID or such other documents; and (ii) enrolling the undersigned in EDGAR Next or any successor filing system;

(2)act as an account administrator for the undersigned’s EDGAR account, including: (i) appointing, removing, and replacing account administrators, technical administrators, account users, and delegated entities; (ii) maintaining the security of the undersigned’s EDGAR account, including modification of access codes; (iii) maintaining, modifying, and certifying the accuracy of information on the undersigned’s EDGAR account dashboard; and (iv) taking any other actions contemplated by Rule 10 of Regulation S-T;

(3)cause the Company to accept a delegation of authority from the undersigned’s EDGAR account administrators and authorize the Company’s EDGAR account administrators pursuant to that delegated entity designation to appoint, remove, or replace users for the undersigned’s EDGAR account;

(4)execute for, and on behalf of, the undersigned, in the undersigned’s capacity as an officer or director of the Company, Forms 3, 4, and 5 relating to the Company in accordance with Section 16(a) of the Exchange Act and the rules and regulations promulgated thereunder and Forms 144 in accordance with Rule 144 under the Securities Act of 1933, as amended (the “Securities Act”);

(5)seek or obtain, as the undersigned’s representative and on the undersigned’s behalf, information on transactions in the Company’s securities from any third party, including brokers, employee benefit plan administrators, and trustees, and the undersigned hereby authorizes any such person to release any such information to any attorney-in-fact and further approves and ratifies any such release of information;

(6)do and perform any and all acts for, and on behalf of, the undersigned that may be necessary or desirable to prepare, complete, and execute any such Forms 3, 4, or 5 or Forms 144 and any amendments thereto or other required reports and timely

file such forms or reports with the SEC, the New York Stock Exchange, and any stock exchange or similar authority as considered necessary or advisable under Section 16(a) of the Exchange Act or Rule 144 under the Securities Act; and

(7)take any other action of any type whatsoever in connection with the foregoing that, in the opinion of such attorney-in-fact, may be of benefit to, in the best interest of, or legally required by, the undersigned, it being understood that the documents executed by such attorney-in-fact on behalf of the undersigned pursuant to this Limited Power of Attorney shall be in such form and shall contain such terms and conditions as such attorney-in-fact may approve in such attorney-in-fact’s sole discretion.

The undersigned hereby acknowledges that: (a) the foregoing attorneys-in-fact are serving in such capacity at the request of the undersigned; (b) this Limited Power of Attorney authorizes, but does not require, each such attorney-in-fact to act in his or her discretion on information provided to such attorney-in-fact without independent verification of such information; (c) any documents prepared or executed by any attorney-in-fact on behalf of the undersigned pursuant to this Limited Power of Attorney shall be in such form and shall contain such information and disclosure as such attorney-in-fact, in his or her sole discretion, deems necessary or advisable; (d) neither the Company nor any attorney-in-fact assumes: (i) any liability for the undersigned’s responsibility to comply with the requirements of the Exchange Act or the Securities Act; (ii) any liability of the undersigned for any failure to comply with such requirements; or (iii) any obligation or liability of the undersigned for profit disgorgement under Section 16(b) of the Exchange Act; and (e) this Limited Power of Attorney does not relieve the undersigned from responsibility for compliance with the undersigned’s obligations under the Exchange Act or the Securities Act, including, without limitation, the reporting requirements under Section 16 of the Exchange Act.

This Limited Power of Attorney shall remain in full force and effect until the undersigned is no longer required to file Forms 3, 4, and 5 or Forms 144 with respect to the undersigned’s holdings of, and transactions in, securities issued by the Company, unless earlier revoked as to any attorney-in-fact by the undersigned in a signed writing delivered to such attorney-in-fact.

[Signature Page Follows]

IN WITNESS WHEREOF, the undersigned has caused this Limited Power of Attorney to be executed as of this 5th day of May, 2025.

By: /s/ Michelle M. Brennan

Name: Michelle M. Brennan

STATE OF OHIO

COUNTY OF FRANKLIN, SS:

On this 5th day of May, 2025, before me, a notary public in and for said county and state, personally appeared Michelle M. Brennan, known to me to be the person who executed the foregoing Limited Power of Attorney, and acknowledged the execution of the same to be her voluntary act and deed.

/s/ Julie A. Gilbert

Julie Gilbert

Notary Public, State of Ohio

My commission expires on June 23, 2028.

[Signature Page to Limited Power of Attorney for SEC Reporting Purposes]

Brennan Michelle 4