It will be Davis' first appearance inside the cage since he suffered his first loss as a professional.
The bout will be part of UFC on Fox 4, which will take place at Staples Center in Los Angeles.
Davis had won each of his first nine pro fights before dropping a unanimous decision Jan. 28 to former 205-pound champion Rashad Evans.
Griggs will make his light heavyweight debut against Davis. While competing at heavyweight, Griggs compiled an 11-2 record.
Nine of Griggs' victories have come by knockout. He never has gone the distance in a fight. In his most recent outing April 21, Griggs was submitted in the first round by Travis Browne.