The Chiefs cut Caldwell on Aug. 12, but Chiefs running backs coach Deland McCullough put in a good word for Caldwell.
"The guy can play," McCullough said last week.
Caldwell had four carries for 59 yards and a touchdown in the Chiefs' game against the Bengals. The Chiefs, though, needed a roster spot to add tight end Manasseh Garner.
The Bears had an opening after cutting kicker Elliott Fry on Sunday.
Caldwell went undrafted out of Northwest Missouri State after rushing for 830 yards on 139 attempts last season.