The move gives the Angels some salary relief, with Fuentes due to earn another $1.89 million in the remaining five weeks. It also helps them replenish a minor league system that has gone from one of the best to one of the weakest over the past few seasons.
Twins manager Ron Gardenhire said he will use Fuentes as a setup man for closer Matt Capps and "probably as an occasional closer if I use the other guy too much."
Capps entered Friday with six saves in eight chances since Minnesota acquired him a trade with Washington last month. The Twins lost closer Joe Nathan before the season began to elbow surgery.
Fuentes, 35, is due to fly from Southern California to join his new team for Saturday's game against the Mariners.
"It's a positive whenever you can acquire a player of his caliber, a closer from another team, to help fill out your bullpen," Gardenhire said.
After the Twins' 6-3 win over the Mariners and the White Sox's 9-4 win over the Yankees on Friday, Minnesota enters Saturday with a 3½-game lead over Chicago in the American League Central.
Fuentes led the majors with 48 saves last season, but he struggled through the first half of this season, in part due to declining velocity. He had a 3.52 ERA and blew four of his 27 save opportunities. He was effective against left-handed batters, who hit just .132 against him.
He becomes the most experienced of the three left-handers Minnesota now has in its bullpen.
"We knew he was out there, and as all players go through waivers, we put in a claim for him along with everyone else," Gardenhire said of Fuentes, who has 542 career appearances. "We got to him first, and he got to us.
"It's another very good arm out in the bullpen, with experience. He should help us a lot, after losing two left-handers recently. ... After we lost Mijares, we've been looking around."
Gardenhire said he was "hoping" Mijares could return from the disabled list in three weeks.
Fuentes will be a free agent after this season. On his way out of Anaheim, he took a shot at Angels fans, who -- perhaps spoiled by previous closers Troy Percival and Francisco Rodriguez -- booed him lustily at times this season.
"It was funny. I felt like I was pitching on the road quite a bit," Fuentes said. "I came in to a lot of boos, but the fans here come out in droves. They're here to be entertained. They're entertained one way or another, through my frustrations or through my success. I felt like I've given them a lot more success than failure."
The Angels signed Fernando Rodney to a two-year, $11 million deal in December in part so he could be their closer in 2011. Now, he'll take over the job a month early. The Angels also have hard throwers Kevin Jepsen and Jordan Walden, who can take over Rodney's eighth-inning duties.
Angels manager Mike Scioscia and general manager Tony Reagins insisted Friday's move wasn't an admission the team is out of contention. They entered Friday's games 9½ games behind the first-place Texas Rangers with 34 games left.
"If we didn't have a guy like Fernando, I think you could make that argument," Scioscia said. "But I feel our bullpen's going to be as strong as we've seen. A lot of guys are going to get the ball with an opportunity to hold leads."
Reagins wouldn't specify the player to be named later but said he is a "prospect with upside."
Mark Saxon covers the Angels for ESPNLosAngeles.com. Information from The Associated Press was used in this report.