First-round choice Donald Brown remains unsigned. Camp for the Colts opens on Sunday but the team is optimistic it will have every draft choice in camp on time.
Moala, who is a 6-foot-4, 305-pound defensive tackle, got a four-year deal. He is expected to see significant playing time for the Colts' defense this season.
Collie is a 6-foot, 200-pound wide receiver.
John Clayton is a senior NFL writer for ESPN.com. The Associated Press contributed to this report.