The 5-foot-11 Avery was a 2008 draft pick of the St. Louis Rams and has 100 catches for 1,263 yards and eight touchdowns in two seasons with the team. He missed the entire 2010 season after tearing his right ACL in an exhibition game against the New England Patriots.
He was cut by the Rams on September 3.
Avery will take the roster spot of receiver Kenny Britt, who was placed on injured reserve after tearing the ACL and MCL in his right knee during the Titans' 17-14 win over the Denver Broncos in Week 3.
Britt had 17 catches for 289 yards and three touchdowns before going down with the injury.