Carreno, 21, went 9-8 with a 3.23 ERA in 27 starts for Class A West Michigan, striking out 119 batters and walking 28 over 139 1/3 innings. He was ranked as the No. 11 prospect in the Tigers' system by MLB.com
The trade is now complete, with the Cubs receiving Carreno and a cash consideration for Baker.
Baker, 31, batted .269 in 54 games with the Cubs before he was dealt to the Tigers. He batted .200 in 15 games with Detroit before he was designated for assignment on Aug. 31, then traded to the Braves. He was 2-for-19 in 14 games with Atlanta.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.