The Indians sent minor league pitcher Jordan Milbrath in exchange for Wittgren. Cleveland designated right-handed pitcher A.J. Cole for assignment to make room for Wittgren on the 40-man roster.
The Marlins selected Wittgren in the ninth round of the 2012 MLB Draft. He made his debut with the Marlins on April 19, 2016, and spent parts of the last three seasons with the club.
The 27-year-old reliever has a 9-5 record with a 3.60 ERA in 118 career relief appearances. Last season, Wittgren pitched 33 2/3 innings across 32 appearances, finishing with a 2.94 ERA and 31 strikeouts.
The Indians selected Milbrath in the 35th round of the 2013 MLB Draft. He played the last six seasons in the franchise's minor league system.