- PHOTOS: Bears 2012 season in pictures
Bennett tweeted Tuesday: "I'm proud to say I'll be joining my other brother @bmarshall next season. #BEARDOWN."
The NFL free agency period officially began at 3 p.m. Tuesday.
The Bears came to terms with Bennett as they look for an offensive tackle as well, but the Vikings Phil Loadholt has apparently decided to stay in Minnesota.
Bennett, 26, experienced a breakout season in 2012, when he caught a career-high 55 passes for 626 yards and five touchdowns, in addition to showing consistency as a run blocker.
Selected in the second round of the 2008 draft by the Dallas Cowboys, Bennett signed a one-year contract worth $2.5 million going into the 2012 season.
New Bears coach Marc Trestman and his offensive staff made it clear upon arrival that the team will now stress versatility from the tight end position.
Also Tuesday, defensive tackle Henry Melton signed his franchise tag tender at $8.45 million.
ESPNChicago contributed to this report.