Brazill was suspended for the first four games last season for violating the substance abuse policy. He said at the time it was for marijuana use.
Brazill played in 10 games last season, finishing with 12 catches for 161 yards and two touchdowns. Over two seasons, including the playoffs, he had 30 catches for 491 yards and five touchdowns. He was drafted in the sixth round out of Ohio University in 2012.
The Colts on Friday also signed free agent wide receiver Aaron Burks, a rookie from Boise State.