Davis, the team's starting tight end over the past two seasons, has been cut by the Bears, they announced Wednesday.
Davis was a scattershot pass-catcher who struggled with drops last season. His 19 catches for 229 yards and two touchdowns in 2012 didn't match up with the two-year, $6 million deal he signed last March.
Bennett, meanwhile, was productive with the New York Giants last season. He's a solid blocker who also generated havoc through the air, pulling down 55 catches for 626 yards and five touchdowns. The Giants didn't prioritize re-signing him, but the Bears saw enough in Bennett to shuffle the lineup and send Davis packing.