Exhibit 5.1

52 East Gay Street

P.O. Box 1008

Columbus, Ohio 43216-1008

614.464.6400 | www.vorys.com

Founded 1909

July 31, 2018

Peoples Bancorp Inc.

138 Putnam Street

P.O. Box 738

Marietta, OH 45750-0738

Ladies and Gentlemen:

We have acted as counsel to Peoples Bancorp Inc., an Ohio corporation (the “Company”), in connection with the Company’s Registration Statement on Form S-8 (the “Registration Statement”) to be filed with the Securities and Exchange Commission on the date hereof in order to register 500,000 common shares, without par value (the “Common Shares”), under the provisions of the Securities Act of 1933, as amended (the “Act”), and the rules and regulations promulgated thereunder (the “Rules and Regulations”), to be issued and delivered under the Peoples Bancorp Inc. Third Amended and Restated 2006 Equity Plan (the “Plan”).

In connection with rendering this opinion, we have examined, to the extent deemed necessary, originals or copies of: (a) the Registration Statement; (b) the Plan; (c) the Company’s Amended Articles of Incorporation, as currently in effect (the “Articles”); (d) the Company’s Code of Regulations, as currently in effect (the “Regulations”); and (e) certain corporate records of the Company, including resolutions adopted by the directors of the Company (and committees thereof) and by the shareholders of the Company. We have also relied upon such oral or written statements and representations of the officers of the Company and examined such certificates of public officials and authorities of law as we have deemed relevant as a basis for this opinion.

In our examination of the aforesaid records, documents and certificates, we have assumed, without independent investigation, the authenticity of all records, documents and certificates examined by us, the correctness of the information contained in all records, documents and certificates examined by us, the genuineness of all signatures, the legal capacity of all individuals who have executed any of the aforesaid documents and certificates, the authority of all individuals entering and maintaining records, and the conformity to authentic originals of all items submitted to us as copies (whether certified, conformed, photostatic or by other electronic means) of records, documents or certificates. In rendering the opinion below, we have further assumed that each award under the Plan will be approved by the Board of Directors of the Company (or a duly authorized committee thereof) and that the agreement that accompanies each award under the Plan will be consistent with the terms of the Plan and will not expand, modify or otherwise affect the terms of the Plan or the respective rights or obligations of any of the participants thereunder.

We have relied solely upon the examinations and inquiries recited herein, and, except for the examinations and inquiries recited herein, we have not undertaken any independent investigation to

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Peoples Bancorp Inc.

July 31, 2018

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determine the existence or absence of any facts, and no inference as to our knowledge concerning such facts should be drawn.

Based upon and subject to the foregoing and subject to the qualifications and limitations set forth herein, as of the date hereof, we are of the opinion that the 500,000 Common Shares to be registered under the Act for issuance and delivery under the Plan, when issued, delivered and paid for, as appropriate, in accordance with, and for the consideration, if any, prescribed in, the Plan and in any award agreements entered into by participants in the Plan with the Company as contemplated by the Plan, will be validly issued, fully paid and non-assessable, assuming compliance with applicable securities laws.

Members of our firm are admitted to the Bar in the State of Ohio and we express no opinion as to the laws of any jurisdiction other than the laws of the State of Ohio, including the applicable provisions of the Ohio Constitution and the reported judicial decisions interpreting those laws, and of the United States of America.

This opinion is based upon the laws and legal interpretations in effect, and the facts and circumstances existing, on the date hereof, and we assume no obligation to revise or supplement this opinion should any such law or legal interpretation be changed by legislative action, judicial interpretation or otherwise or should there be any change in such facts or circumstances.

This opinion is furnished by us solely for the benefit of the Company in connection with the offering of the 500,000 Common Shares covered by the Registration Statement pursuant to the Plan and the filing of the Registration Statement and any amendments thereto.

Notwithstanding the foregoing, we consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to us therein. By giving such consent, we do not thereby admit that we come within the category of persons whose consent is required under Section 7 of the Act or the Rules and Regulations.

Except in connection with the Registration Statement as aforesaid, no portion of this opinion may be quoted or otherwise used by any person without our prior written consent.

Sincerely,

/s/ Vorys, Sater, Seymour and Pease LLP