The Indians also sent cash with Shoppach to the Rays in the Dec. 1 deal.
The 26-year-old Talbot was limited to 10 starts last season at Triple-A Durham because of a strained elbow. The right-hander went 4-4 with a 4.47 ERA and was able to finish the year on a positive note by making two starts in the International League playoffs.
Talbot was drafted by Houston in 2002 and traded to Tampa Bay in 2006 for Aubrey Huff. He appeared in three major league games for the Rays in 2008.
The Indians also signed reliever Saul Rivera to a minor league contract and invited him to spring training. Rivera made a franchise-record 245 appearances for Washington from 2006-09. He played for new Cleveland manager Manny Acta with the Nationals.