The deal was completed by general manager Bill Smith about four hours before Friday's 6-3 win over the Mariners. Smith called Gardenhire at about 4 p.m PT.
Fuentes, 34, had been the closer for the Angels, with 23 saves this season and a league-leading 48 last year.
He was 4-1 with a 3.52 ERA in 39 appearances this season, and will join the Twins in time for Saturday afternoon's game with the Mariners.
"He'll be setup and probably occasionally close if I use [Matt Capps] too much," Gardenhire said.
Capps was acquired from Washington on July 29. He has six saves in eight opportunities.
What matters most to Gardenhire is that he has another left-hander at his disposal. The Twins already lost a couple lefties, one for the season, Ron Mahay (rotator cuff), and one they hope to get back in mid-September, Jose Mijares (knee).
"He gets lefties out pretty [darn] good, plus he can close, too," Gardenhire said. "Another very, very good arm out in the bullpen with experience. He should help us out."
Left-handed batters are hitting just .132 against Fuentes this season, 5-for-38 with one extra-base hit (double).
"It's a positive when a player of his caliber is acquired to help fill out your bullpen," Gardenhire added. "When you lose players in trades that can shake you up a little bit. We're adding. We trying to get better, which is what we said we were trying to do."
This is the fourth team for Fuentes. He was originally drafted by Seattle in the 25th round in 1995. He was traded to Colorado in 2001 and signed a free-agent deal with Los Angeles in '09. His contract ends this year.
With the acquisition of Fuentes, the Twins made a roster move after Friday's game, sending left-hander Glen Perkins to Triple-A.
"That's a good thing for him," Gardenhire said. "He's sitting out there, not doing a lot. And we've got a couple lefties now. It'll be good to get him pitching."