Parker's deal includes an invitation to training camp in Arizona, where Cleveland will try to upgrade its relief corps to complement a solid starting staff.
Parker, 35, spent the past two seasons with the Philadelphia Phillies. In 14 games last season, the right-hander went 3-0 with a 2.81 ERA. He has also pitched for the Cubs, Mariners, Yankees, Angels and Twins in eight major league seasons.
Parker has 34 career saves in 303 games. He's 14-10 with a 3.52 ERA since breaking in with Chicago in 2012.
At this point, the Indians will have 14 non-roster invitees in camp, which opens this week.