Costanzo, a five-year NFL veteran, spent 2011 with San Francisco after previous stops in Cleveland, Buffalo and the New York Jets. Costanzo's two-year deal is worth $2.2 million with a $400,000 signing bonus.
The former undrafted rookie free agent out of Lafayette ranked second on the 49ers last season with 17 special-teams tackles. Costanzo made two memorable plays in San Francisco's playoff victory over New Orleans, forcing a fumble on a punt and recovering a fumble on a kickoff.
The move protects the Bears in the event Pro Bowl special teamer Corey Graham departs via free agency. Graham is expected to generate interest from several teams.