Graham King and Tim Headington will produce with Frankie Valli and Bob Gaudio serving as executive producers.
The project is likely to be set up at Columbia Pictures for most of worldwide distribution rights while GK Films will hold back select territories.
Logan collaborated with GK Films recently on the acclaimed Hugo. Jersey Boys tells the story of Frankie Valli And The Four Seasons.
The stage show has sold more than $1bn in tickets worldwide and it is anticipated that the feature will use much of the same music and lyrics from the play.
“Frankie, Bob, Marshall, Rick, Amy, Tim and I are very excited about making this award-winning musical,” King said. “As a group, we collectively decided to go to John to adapt this incredible story.”