Exhibit 5.1

ADC Therapeutics SA Biopôle Route de la Corniche 3 B 1066 Epalinges Switzerland Homburger AG Prime Tower Hardstrasse 201 | CH–8005 Zurich   T  +41 43 222 10 00 F  +41 43 222 15 00 lawyers@homburger.ch

May 14, 2020

ADC Therapeutics SA – Registration Statement on Form F-1

Ladies and Gentlemen

We have acted as special Swiss counsel to ADC Therapeutics SA, a stock corporation incorporated under the laws of Switzerland (the Company), in connection with the filing of a registration statement on Form F-1, including the prospectus set forth therein (the Registration Statement), to be filed with the United States Securities and Exchange Commission (the SEC) on the date hereof for the purpose of registering under the United States Securities Act of 1933, as amended (the Securities Act), the offer and sale of up to 11,839,250 common shares of the Company, each with a nominal value of CHF 0.08 (the Common Shares), including any common shares with a nominal value of CHF 0.08 each to be sold, if and to the extent such option is exercised, to the underwriters pursuant to the over-allotment option granted by the Company to the underwriters. As such counsel, we have been requested to give our opinion as to certain legal matters of Swiss law.

Capitalized terms used but not defined herein shall have the meaning ascribed to them in the Documents (as defined below).

I. Basis of Opinion

This opinion is confined to and given on the basis of the laws of Switzerland in force at the date hereof. Such laws and the interpretation thereof are subject to change. In the absence of explicit statutory law, we base our opinion solely on our independent professional judgment. This opinion is also confined to the matters stated herein and is not to be read as extending, by implication or otherwise, to any document referred to in the Documents (other than listed below) or any other matter.

For purposes of this opinion we have not conducted any due diligence or similar investigation as to factual circumstances, which are or may be referred to in the Documents, and we express no opinion as to the accuracy of representations and warranties of facts set out in the Documents or the factual background assumed therein.

For purposes of this opinion, we have only reviewed originals or copies of the following documents we have deemed necessary or advisable for the purpose of rendering this opinion (collectively the Documents):

(i) an electronic copy of the Registration Statement;

(ii) an electronic copy of the notarized shareholders’ resolutions passed at the Company’s extraordinary general meeting held on April 24, 2020 (the Shareholders’ Resolutions); and

(iii) an electronic copy of the articles of association (statuts) of the Company, the form of which is filed as Exhibit 3.1 to the Registration Statement (the Articles of Association).

No documents, other than the Documents, have been reviewed by us in connection with this opinion. Accordingly, we shall limit our opinion to the Documents and their legal implications under Swiss law.

In this opinion, Swiss legal concepts are expressed in English terms and not in their original language. These concepts may not be identical to the concepts described by the same English terms as they exist under the laws of other jurisdictions.

2 | 4

II. Assumptions

In rendering the opinion below, we have assumed the following:

(a) all documents produced to us as originals are authentic and complete, and all documents produced to us as copies (including, without limitation, electronic copies) conform to the original;

(b) all documents produced to us as originals and the originals of all documents produced to us as copies were duly executed and certified, as applicable, by the individuals purported to have executed or certified, as the case may be, such documents;

(c) all documents produced to us in draft form will be executed in the form of the draft submitted to us;

(d) each party to the Documents is a corporation or other legal entity duly organized and validly existing and in good standing (if applicable) under the laws of the jurisdiction of its incorporation and|or establishment and none of the parties to the Documents (other than the Company) has passed or, until the issuance of all Common Shares, will have passed a voluntary winding-up resolution; no petition has been, or, until the issuance of all Common Shares, will be presented or order made by a court for the winding-up, dissolution, bankruptcy or administration of any party (other than the Company); and no receiver, trustee in bankruptcy, administrator or similar officer has been or, until the issuance of all Common Shares, will have been appointed in relation to any of the parties (other than the Company) or any of their assets or revenues;

(e) to the extent relevant for purposes of this opinion, any and all information contained in the Docu-ments is and will be true, complete and accurate at all relevant times;

(f) no laws (other than those of Switzerland) affect any of the conclusions stated in this opinion;

(g) the Registration Statement is unchanged and correct, complete and up-to-date and in full force and effect as of the date hereof and no changes have been made which should have been or should be reflected in the Registration Statement as of the date hereof;

(h) The Shareholders' Resolutions (i) have been duly resolved in a meeting duly convened and otherwise in the manner set forth therein, (ii)  have not been amended and (iii) are  in full force and effect;

(i) prior to the issuance of any Common Shares, the board of directors of the Company will have duly authorized the issuance and sale of such Common Shares and will have validly excluded the pre-emptive rights of the existing shareholders for purposes of offering and selling the Common Shares as contemplated in the Registration Statement, and such authorization will not have been amended and will be in full force and effect until the issuance of all Common Shares;

(j) the Company has not entered and will not enter into any transaction which could be construed as repayment of share capital (réstitution des versements) and has not undertaken and will not undertake an acquisition in kind (reprise des biens) or intended acquisition in kind (reprise des biens envisagée) without complying with the formal procedure set forth in article 628 of the Swiss Code of Obligations; and

3 | 4

(k) all authorizations, approvals, consents, licenses, exemptions, other than as required by mandatory Swiss law applicable to the Company or the Articles of Association, and other requirements for the filing of the Registration Statement or for any other activities carried on in view of, or in connection with, the performance of the obligations expressed to be undertaken by the Company in the Registration Statement have been duly obtained or fulfilled in due time and are and will remain in full force and effect, and any related conditions to which the parties thereto are subject have been satisfied.

III. Opinion

Based on the foregoing and subject to the qualifications set out below, we are of the opinion that the Common Shares, when issued and paid for pursuant to the Articles of Association and Swiss law, in particular upon registration of the corresponding share capital increase into the Commercial Register of the Canton of Vaud, and entered into the Company’s book of uncertificated securities, will be validly issued, fully paid as to their nominal value and non-assessable.

IV. Qualifications

The above opinions are subject to the following qualifications:

(a) The lawyers of our firm are members of the Zurich bar and do not hold themselves out to be experts in any laws other than the laws of Switzerland. Accordingly, we are opining herein as to Swiss law only and we express no opinion with respect to the applicability or the effect of the laws of any other jurisdiction to or on the matters covered herein.

(b) The exercise of voting rights and rights related thereto with respect to any Common Shares is only permissible after registration in the Company’s share register as a shareholder with voting rights in accordance with the provisions of, and subject to the limitations provided in, the Articles of Association.

(c) We express no opinion as to whether the Registration Statement is accurate, true, correct, complete or not misleading. In particular, and without limitation to the foregoing, we express no opinion on whether the Registration Statement provides sufficient information for investors to reach an informed assessment of the Company, any companies within the Company’s consolidation perimeter and the Common Shares.

(d) Notwithstanding or irrespective of registration of the capital increase with the Commercial Register of the Canton of Vaud, the underlying shareholders’ resolutions may be challenged by a dissenting shareholder of the Company or others in court or otherwise. However, we believe that a challenge of the underlying shareholders’ resolution by a dissenting shareholder of the Company after registration of the Common Shares with the Commercial Register of the Canton of Vaud, even if successful, would not in itself void such Common Shares.

(e) We express no opinion as to regulatory matters or as to any commercial, accounting, calculating, auditing or other non-legal matter.

We have issued this opinion as of the date hereof and we assume no obligation to advise you of any changes in fact or in law that are made or brought to our attention hereafter.

4 | 4

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and further consent to the reference to our name under the caption “Legal Matters” in the Prospectus. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

This opinion is governed by and shall be construed in accordance with the laws of Switzerland.

Sincerely yours

Homburger AG

/s/ Benjamin Leisinger