Quinn, who turns 30 in May, signed a five-year deal worth up to $70 million that includes $30 million guaranteed, as NFL Media initially reported.
Quinn is a nine-year NFL veteran who has 80.5 sacks over 125 career games. He played for the Cowboys last season, posting 11.5 sacks.
The Bears on Wednesday also completed their contract with offensive lineman Germain Ifedi, who signed a one-year deal.
The completion of contracts had been delayed due to the coronavirus global pandemic. The Bears have now completed all of the deals that they previously agreed to with free agents.