Indians general manager Chris Antonetti made the announcement Thursday, one day after the team finished Acta's second season with an 80-82 record.
Acta, the former Washington Nationals manager, was hired by Cleveland in October 2009 to replace the fired Eric Wedge, signing a three-year contract with a club option for the fourth year.
He is 149-175 in two seasons as Indians manager. The club got off to a major league-best 30-15 start this year, but were only five games over .500 by the All-Star break and went seven games under .500 in the second half.
Cleveland finished second in the AL Central, 15 games behind the Detroit Tigers.
Also on Thursday, pitching coach Tim Belcher stepped down as pitching coach, saying he could no longer balance the needs of his family life with the demands of the job.
Belcher will assume a position similar to the special assistant to baseball operations role he served for eight seasons before becoming pitching coach in 2010.