The 27-year-old has appeared in 51 games with 22 starts over four seasons with the New Orleans Saints (2013-16) and Seattle Seahawks (2016), recording 113 tackles, 1.5 sacks, two pass breakups, six tackles-for-loss, one forced fumble and one fumble recovery.
Jenkins was selected by the Saints in the third round of the 2013 draft out of Georgia when Bears general manager Ryan Pace worked in New Orleans' personnel department.
The 6-3, 359-pounder was released by the Saints last Nov. 9 and signed by the Seahawks Nov. 15. Jenkins played in nine games with one start last year, registering 13 tackles.