Correia was told late Saturday after the Twins' 9-4 loss at Oakland that he was headed home to Southern California to be part of a pennant race in the familiar NL West.
Minnesota will call up left-hander Tommy Milone from Triple-A Rochester to start Monday at Houston. Milone was acquired from the Athletics on the July 31 trade deadline after he requested to be moved following a demotion to the minors. Minnesota sent outfielder Sam Fuld back to Oakland in the swap.
A fourth-round draft pick by San Francisco in 2002, Correia (5-13, 4.94 ERA) has pitched for the Giants and San Diego Padres.
"It's nice to be able to go somewhere and play some important baseball games at the end of this year and it's a place I'm very familiar with, so it's exciting," Correia said after saying his goodbyes to Twins teammates at his locker. "It's why we play this game.
"I'm getting toward the end of my career and you want to play in some meaningful games and I'll have the opportunity to do that over there."
The NL West-leading Dodgers, who lost earlier Saturday at Milwaukee, were looking to boost the back end of their rotation.
Beckett, who is 6-6 with a 2.88 ERA in 20 starts for the Dodgers this season, has a left hip impingement. The move is retroactive to Aug. 4. He is expected to be out about two weeks. The 14-year veteran made three starts since being reinstated on July 22 from the same injury, which occurred on July 8. His first time on the disabled list was March 22 when he had a right-thumb contusion.
Correia has ties to general manager Ned Colletti, the former Giants assistant GM, and medical director Stan Conte.
"It's a division I'm familiar with and there's a couple of familiar faces from when I was with the Giants: Ned Colletti and Stan Conte, the trainer," Correia said. "So it's not going to be a completely foreign situation for me and I think that'll help."
Twins manager Ron Gardenhire praised Correia for his work with the club over two seasons in spite of his struggles with a career-high losses this year.
"He's been nothing but a pleasure. Last year he was our best pitcher, most consistent pitcher," Gardenhire said. "This year I know he had some ups and downs but he always seemed to give us a chance. A great guy in the clubhouse. ... It's a good situation. He's going to a team in the pennant race. He deserves it."
The 27-year-old Milone made one start at Triple-A on Aug. 5, allowing one run on six hits in seven innings.
"We are really excited to get him. We didn't want to give up Sammy Fuld," Gardenhire said. "We got a nice pitcher out of the deal, a guy that knows how to pitch in the big leagues, good track record. We're going to get him up here. ... We've made a spot now, and he's going to get the ball."