The tight end was a free agent after failing to reach a new deal with the New York Giants, where he had spent last season.
General manager Phil Emery told the Bears' website: "He's a very good athlete with excellent size. He's a good receiver who runs good routes, and he's a good blocker who still has upside in that area, to use that size and strength that he has to be an even better blocker.
"I see a player who has matured since coming out of Texas A&M, and he proved that with his production and his play this past year.
"He's someone who still has a lot of upside to develop. Because of his athletic ability and play speed, we think he's only going to get better and grow as a Bear and help us win football games."
Bennett scored five touchdowns for 626 yards last year.