The 6-2, 192-pounder has appeared in 53 NFL games with 24 starts over four seasons with the Kansas City Chiefs (2013-15) and Arizona Cardinals (2016), recording 130 tackles, seven interceptions, 32 pass breakups, one forced fumble and one fumble recovery.
Cooper, 27, is the fourth defensive back to sign with the Bears in a little over 24 hours; they inked safety Quintin Demps Friday and cornerbacks Prince Amukamara and Johnthan Banks earlier Saturday.
Last season with the Cardinals, Cooper set career highs with 15 games played, 13 starts, 69 tackles and four interceptions.