Acta, 40, was one of three people interviewed by the Indians to replace Eric Wedge.
Acta signed a three-year contract with a club option for 2013, team spokesman Bart Swain said Sunday. Additional terms were not disclosed.
"I am very excited to become part of the Cleveland Indians family," Acta said. "I look forward to working with this talented group of young men who seem to possess a lot of energy and passion for their work."
Acta managed the Nationals for 2½ seasons, compiling a 158-252 record before being replaced this past July. He had also interviewed for the vacant Astros managing job.
"We are very excited to have Manny Acta on board as our major league manager," Indians general manager Mark Shapiro said in a statement.
"After speaking with an impressive array of candidates, we feel that Manny is a very strong and experienced leader who possesses great energy and enthusiasm along with tremendous communication skills and a positive mindset that will command a presence in the dugout, clubhouse and with our fans."
The Indians had talked seriously with veteran manager Bobby Valentine, but Valentine apparently could not quickly assure them that he would take the job. Valentine is working at ESPN as an analyst and may be in position to pick and choose his spot.
The Nationals also are interested in Valentine but there's no certainty he'll jump at that job either, if it's offered. Longtime Indians minor league manager Torey Lovullo had also interviewed for the job. Don Mattingly, the likely heir apparent to Joe Torre in Los Angeles and a managerial candidate in Washington, had been expected to interview this week.
While Acta was just 26-61 as manager of the Nationals this season, he is highly regarded and was said to be a finalist for the Astros' vacant job, as well. Other contenders in Houston include interim manager Dave Clark, ex-Astros manager Phil Garner and Red Sox bench coach Brad Mills.
The Indians acted fast in hiring Acta after conducting in-person interviews this past week. Acta is a nice fit for an organization heavy on Latin players.
"He's certainly deserving of being a manger, and he will be a manager again,'' Nationals president Stan Kasten said Sunday morning when it became clear Acta was likely to land the Indians job. "Manny is so intelligent, and so articulate. And he's very good with players. He's very active. He was out there hitting fungos (while managing the Nationals). He has a lot going for him.''
Cleveland tied for last in the AL Central with a 65-97 record after coming into this year with high expectations. The Indians fired Wedge in the final week of the season.