Tatum, 37, will serve as a producer on the "X-Men" spin- off with his partner Reid Carolin through their Free Association production company, along with Simon Kinberg.
Following Verbinski's exit over scheduling issues, Fox has pushed back the release date of the film from February 14, 2019, to June 7, 2019, according to The Hollywood Reporter.
Rupert Wyatt and Doug Liman were previously attached as directors on the project.
The Gambit's character, also known as Remy LeBeau, was created in 1990 by Chris Claremont and Jim Lee, a mutant who is an expert card-thrower with the ability to mentally create, control and manipulate kinetic energy.