Exhibit 99.4

Consent of James H. Miller to be Named as a Director

Pursuant to Rule 438 promulgated under the Securities Act of 1933, as amended, I, the undersigned, hereby consent to my being named in the Registration Statement on Form S-4 of Leo Holdings Corp., and all amendments, including post-effective amendments thereto (the “Registration Statement”), as a person about to become a director of Digital Media Solutions, Inc. upon completion of the Business Combination and the other transactions described in the Registration Statement.

Dated: May 11, 2020

/s/ James H. Miller

James H. Miller