The Animal Kingdom star will take on the role of a special operative commanded to kill the leader of al-Qaida after the terrorist attacks on 9/11, 24 Frames reports.
According to the site, the script by Hurt Locker writer Mark Boal has been rejigged in light of the terrorist's death.
It will now feature a sequence ending with a successful attack on Bin Laden.
Edgerton has just finished filming the mixed martial arts-themed Warrior, which also stars Nick Nolte and Tom Hardy, and is slated for a September release.
He reportedly tested for the lead in the next Bourne film last month.