Having made his big-screen directorial debut on sci-fi movie Chronicle, Trank has previously worked on the television drama The Kill Point.
Rumors that 20th Century Fox executives were eyeing Trank to helm a remake of the movie franchise first emerged in January.
Fox has previously released two Fantastic Four movies, directed by Tim Story. Chris Evans, Jessica Alba, Ioan Gruffudd and Michael Chiklis starred in the lead roles.
According to Deadline, Trank has now finalised negotiations to take on the project, which will have a brand new cast.
Trank has another comic book property lined up to direct, Warner Bros. upcoming The Red Star.
Watch a clip from Josh Trank's Chronicle below: