In his second season with Cleveland, the 33-year-old Aviles batted .247 with 16 doubles, five homers and 39 RBIs in 113 games. He added 14 steals, matching a career high.
Cleveland went 48-40 in games Aviles started. He played six positions, including 28 games at third base and second.
Aviles was acquired in a trade from Toronto in 2012, coming over in the deal that also brought the Indians catcher Yan Gomes. If the option had been declined, Aviles would have been owed a $250,000 buyout.
Cleveland also promoted Ross Atkins to vice president of player personnel, Carter Hawkins to director of player development and Paul Gillispie to director of pro scouting. Atkins has spent the past eight seasons leading the club's player development system. He started with the organization in 1995.