The Warrior star was first connected to the untitled project in May 2011, but has now negotiated a deal, reports Variety.
The film will deal with the black ops SEAL team that headed the successful hunt for the Al-Qaeda leader.
Jessica Chastain, Edgar Ramirez and Mark Strong are negotiating for roles in the cast, according to Deadline.
Idris Elba, Rooney Mara, Jennifer Ehle, Guy Pearce, Nina Arianda and Tom Hardy were formerly rumoured to be in talks for the film, but it is unclear which of those actors remain in the running.
Edgerton previously told Digital Spy that development of the film might need to wait to give history "time to settle".
Watch Joel Edgerton discuss the Bin Laden project with Digital Spy below: