Law recently quit the project after the low-budget western's original director, Lynne Ramsey, left because of creative and contract issues. Director Gavin O'Connor took over for Ramsey.
The film stars Natalie Portman as a woman defending her farm after her outlaw husband's gang tries to kill him. Joel Edgerton plays her ex-lover, who helps her, while Cooper will play the villainous leader of the gang.
Cooper was nominated for an Oscar for his work in 2012's "Silver Linings Playbook."
Notable deaths of 2014 [PHOTOS]
'Vacation' re-boot starts shooting in Georgia