Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in Origin Bancorp, Inc.’s Registration Statement (No. 333-234068) on Form S-3 (the Registration Statement) of our report dated February 28, 2020, on our audits of the consolidated financial statements of Origin Bancorp, Inc. as of December 31, 2019 and 2018, and for each of the years in the three-year period ended December 31, 2019, which report is included in the Company’s Annual Report on Form 10-K for the year ended December 31, 2019. We also consent to the incorporation by reference of our report dated February 28, 2020, on our audit of the internal control over financial reporting of Origin Bancorp, Inc. as of December 31, 2019, which report is included in such Annual Report on Form 10-K. We also consent to the reference to our firm under the caption “Experts” in this Registration Statement.

/s/ BKD, LLP

Little Rock, Arkansas

October 7, 2020