The veteran right-hander will get a chance to start with Cleveland, a team in need of a strong rotation.
The Tribe had a terrible 2012 when it came to its starting rotation, which posted the second-highest ERA in the American League at 5.25, and that's why they have been looking for new options on the market.
Myers has pitched more recently as a reliever, doing setup and closing work. He appeared in such duties last season for the Astros and White Sox, for a total of 70 appearances. He was a starter for Houston in 2011, with a 7-14 record in 216 innings of work.
Justin Masterson, Ubaldo Jimenez, Zach McAllister and Myers are poised to become the top four starters for the Indians next season; with names such as Carlos Carrasco, Jeanmar Gomez, David Huff and Corey Kluber competing for the fifth spot.