Ratliff started four of five games played after signing with the team in November, producing 14.5 tackles, 1.5 sacks and a tackle for a loss.
Over nine years with Dallas (2005-12) and Chicago, Ratliff, a four-time Pro Bowler (2008-2011) started 89 of 109 games, recording 331.5 tackles, including 28.5 sacks and 26 tackles for lost yardage. He also has 13 fumble recoveries and five forced fumbles.
A former Cowboys 2005 seventh-round draft pick (224th overall), Ratliff has appeared in at least 15 games in six (2006-11) of his nine NFL seasons, starting all 16 in four of those seasons.
The Bears have now signed 10 players set to hit unrestricted free agency on March 11, a number that registers as the most of any team in the NFL.