Exhibit 5.1

February 7, 2017

Cardinal Health, Inc.7000 Cardinal Place
Dublin, OH 43017

Re: Cardinal Health, Inc.
Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to Cardinal Health, Inc., an Ohio corporation (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of a Registration Statement on Form S-3 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration under the Securities Act and the proposed issuance and sale from time to time pursuant to Rule 415 under the Securities Act, together or separately and in one or more series (if applicable) of:

(i)the Company’s common shares, without par value (the “Common Shares”);

(ii)the Company’s preferred shares, without par value (the “Preferred Shares”); and

(iii)the Company’s unsecured debt securities, which may either be senior debt securities or subordinated debt securities (the “Debt Securities”).

The Common Shares, Preferred Shares and Debt Securities are collectively referred to herein as the “Securities.” The Debt Securities are to be issued under an indenture (the “Base Indenture”) entered intobetween the Company and The Bank of New York Mellon Trust Company, N.A. (formerly The Bank of New York Trust Company), as indenture trustee.

In arriving at the opinion expressed below, we have examined originals, or copies certified or otherwise identified to our satisfaction as being true and complete copies of the originals, of the Base Indenture, forms of the Debt Securities and such other documents, corporate records, certificates of officers of the Company and of public officials and other instruments as we have deemed necessary or advisable to enable us to render this opinion. In our examination, we have assumed the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies. As to any facts material to this opinion, we have relied to the extent we deemed

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appropriate and without independent investigation upon statements and representations of officers and other representatives of the Companyand others.

We are not admitted or qualified to practice law in the State of Ohio. Therefore, we have relied upon the opinion of John M. Adams, Jr., Associate General Counsel of the Company, with respect to matters governed by the laws of the State of Ohio.

We have assumed without independent investigation that:

(i)at the time any Securities are sold pursuant to the Registration Statement (the “Relevant Time”), the Registration Statement and any supplements and amendments thereto (including post-effective amendments) will be effective and will comply with all applicable laws;

(ii)at the Relevant Time, a prospectus supplement will have been prepared and filed with the Commission describing the Securities offered thereby and all related documentation and will comply with all applicable laws;

(iii)all Securities will be issued and sold in the manner stated in the Registration Statement and the applicable prospectus supplement;

(iv)at the Relevant Time, all corporate or other action required to be taken by the Company to duly authorize each proposed issuance of Securities and any related documentation (including (i) the due reservation of any Common Shares or Preferred Shares for issuance upon exercise, conversion or exchange of any Securities for Common Shares or Preferred Shares (a “Convertible Security”), and (ii) the execution (in the case of certificated Securities), delivery and performance of the Securities and any related documentation referred to in the opinion below) shall have been duly completed and shall remain in full force and effect;

(v)upon issuance of any Common Shares or Preferred Shares upon exercise, conversion or exchange of any Convertible Security, the total number of Common Shares or Preferred Shares issued and outstanding will not exceed the total number of Common Shares or Preferred Shares, as applicable, that the Company is then authorized to issue under its articles of incorporation and other relevant documents;

(vi)in the case of Debt Securities, at the Relevant Time, the Base Indenture shall have been duly qualified under the Trust Indenture Act of 1939; and

(vii)at the Relevant Time, a definitive purchase, underwriting or similar agreement and any other necessary agreement with respect to any Securities offered or issued will have

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been duly authorized by all necessary corporate or other action of the Company and duly executed and delivered by the Company and the other parties thereto.

Based on the foregoing and in reliance thereon, and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that, with respect to any Debt Securities, when:

a. the terms and conditions of such Debt Securities have been duly established by supplemental indenture or officers’ certificate in accordance with the terms and conditions of the relevant Base Indenture,

b. any such supplemental indenture has been duly executed and delivered by the Company and the relevant trustee (together with the relevant Base Indenture, the “Indenture”), and

c. such Debt Securities have been executed (in the case of certificated Debt Securities), delivered and authenticated in accordance with the terms of the applicable Indenture and issued and sold for the consideration set forth in the applicable definitive purchase, underwriting or similar agreement,

such Debt Securities will be legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms.

The opinion expressed above is subject to the following exceptions, qualifications, limitations and assumptions:

A.We render no opinion herein as to matters involving the laws of any jurisdiction other than the State of New York. This opinion is limited to the effect of the current state of the laws of the State of New York and the facts as they currently exist. We assume no obligation to revise or supplement this opinion in the event of future changes in such laws or the interpretations thereof or such facts.

B.The opinion above is subject to (i) the effect of any bankruptcy, insolvency, reorganization, moratorium, arrangement or similar laws affecting the rights and remedies of creditors’ generally, including without limitation the effect of statutory or other laws regarding fraudulent transfers or preferential transfers, and (ii) general principles of equity, including without limitation concepts of materiality, reasonableness, good faith and fair dealing and the possible unavailability of specific performance, injunctive relief or other equitable remedies regardless of whether enforceability is considered in a proceeding in equity or at law.

C.We express no opinion regarding the effectiveness of (i) any waiver of stay, extension or usury laws; (ii) provisions relating to indemnification, exculpation or

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contribution, to the extent such provisions may be held unenforceable as contrary to public policy or federal or state securities laws; or (iii) any provision to the effect that every right or remedy is cumulative and may be exercised in addition to any other right or remedy or that the election of some particular remedy does not preclude recourse to one or more others.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Validity of the Securities” in the Registration Statement and the prospectus that forms a part thereof. In giving these consents, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ GIBSON, DUNN & CRUTCHER LLP