Perry led the Bears with 17 special-teams tackles in 2014 after signing as an undrafted free agent. He missed last season because of a foot injury.
The Bears waived defensive lineman Keith Browner, receiver Kieran Duncan, receiver Derek Keaton, offensive lineman John Kling, receiver Darrin Peterson, defensive back Joel Ross, tight end Gannon Sinclair and offensive lineman Martin Wallace on Sunday. They also terminated the contract of vested veteran fullback Darrell Young.
The moves trimmed Chicago's roster to 80 active players. Rosters must be at 75 players by Tuesday.