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."