The 32-year-old has spent parts of eight years in the big leagues and has a 4.21 ERA over the course of 408 1/3 innings. He recorded 316 strikeouts compared to 150 walks and is best known for his work with the Tigers from 2010-14.
Coke will begin his tenure with the Blue Jays in the Minors, but there's a chance he could pitch his way onto the roster before too long. Toronto has struggled to get a lot of production from its relievers and there has been a need for a third lefty to pair with closer Brett Cecil and set-up man Aaron Loup.
With Cecil limited to pitching in the ninth, Loup has been the only lefty that Blue Jays manager John Gibbons has been able to use in the middle innings. That would seem to make the pairing with Coke a perfect fit, but he'll need to put up better numbers than he did with the Cubs to secure a spot.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, follow him on Twitter @gregorMLB and Facebook, and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.