Financial terms weren't immediately available.
The 6-foot-3, 359-pound Jenkins has been a run-stopper through his first four NFL seasons. He has 118 career tackles and 1.5 sacks.
Jenkins spent his first 3 1/2 seasons with the New Orleans Saints until he was released after seven games last season. He joined the Seattle Seahawks and played in two games before becoming a free agent.
He figures to compete for a backup spot behind starting nose tackle Eddie Goldman.
Jenkins was a third-round draft pick in 2013 when current Bears general manager Ryan Pace was the Saints' director of player personnel.