The 33-year-old Floyd hasn't pitched a full Major League season since 2012 because of various injuries. He posted a 2.70 ERA in seven relief appearances for the Indians in 2015 after returning from a right elbow injury.
Floyd was a consistent cog in the White Sox's rotation from 2008-12, making at least 29 starts in every season.
He is 72-72 with a 4.38 ERA in 215 games (196 starts) in 12 years with the Phillies, White Sox, Braves and Indians.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth.