The Bears will play the Cowboys on Dec. 9, meaning Ratliff likely will attempt to sack former teammate Tony Romo.
Dallas released Ratliff two weeks ago, citing a failed physical.
Ratliff, 32, has not played in nearly a year after suffering a groin injury that led him to eventual sports hernia surgery in December.
Initially, the Bears weren't interested when Ratliff was first released because they believed his injury was so severe he couldn't help them this season. But when more information came about Ratliff's condition, the Bears decided to bring him in to have their own doctors take a look at him.
The primary factor in Ratliff choosing the Bears over the Chiefs was that Chicago plays the 4-3 scheme and offered the potential to be a starter and earn significant playing time following Henry Melton's season-ending injury. Ratliff, a four-time Pro Bowler, is projected to be ready to play in two to four weeks.
Ratliff is seeking to re-establish himself since he hasn't played in the NFL since late last season. He will be an unrestricted free agent after this year.
It's an acknowledgement of the skills Ratliff possessed and still may have that the Bears, Chiefs and Dolphins all made contract offers before he was healthy enough to play.
Ratliff has familiarity with several members of Marc Trestman's coaching staff in Chicago, including special teams/assistant head coach Joe DeCamillas and running backs coach Skip Peete, both of whom were previously in Dallas.
Ratliff faces charges of driving while intoxicated stemming from an arrest earlier this year, six weeks after then-Cowboys backup Josh Brent's crash, which killed teammate Jerry Brown Jr. Ratliff's trial has been postponed until February.
Information from ESPN.com's Michael C. Wright was used in this report.