Quinn is signing a five-year, $70 million contract with the Bears, Ian Rapoport of NFL Network reports.
Quinn finished the 2019 season with 34 tackles (26 solo) including 11.5 sacks, three passes defended and two forced fumbles in 14 games.
Quinn notched six tackles (five solo) and a sack in Sunday's 17-9 loss to the Eagles.
Quinn recorded no tackles in Sunday's win over the Rams.
Quinn recorded five tackles (four solo) during Thursday's 31-24 loss to the Bears.
Quinn had one assisted tackle, one sack and a forced fumble during Sunday's 13-9 loss to the Patriots.
Quinn collected three tackles (three solo) and a sack in Sunday's 35-27 win over the Lions
Quinn registered three tackles (one solo) and a sack in Sunday's loss to the Vikings.
Quinn (ribs) was a full participant in Thursday's practice, David Helman of the Cowboys' official site reports.
Quinn (ribs) is expected to return to practice this week and be ready to play the Giants on Monday night, Jon Machota of The Athletic reports.