The club officially announced the signing Wednesday morning after Capps passed his physical on Tuesday.
The Twins did not offer specifics on the terms of the deal, but according to The Associated Press, Capps is set to earn $4.5 million this year, and the contract includes a $6 million option for 2013 with a $250,000 buyout.
Capps, 28, posted a 4.25 ERA with 34 strikeouts, 13 walks and 10 homers allowed in 65 2/3 innings with the Twins last season. He also converted 15 saves in 24 opportunities, as he lost his role as closer to Joe Nathan after struggling in mid-July.
"He was a little sore, but he always took the ball," Twins general manager Terry Ryan said. "He never made excuses. If you listened to that [conference call], people are concerned about us bringing back Matt Capps, and I said, 'Well, people have an off year.' He had an off year, as did the club."
But the Twins liked Capps' attitude and said the right-hander pitched hurt most of the season, dealing with a forearm issue.
"You never heard him complain about his forearm," Ryan said. "He never complained or backed off. I don't know how severe it was. But it's obviously not a big issue with us [now]."
Capps is expected to be the closer next season, with left-hander Glen Perkins likely to remain in a setup role. Nathan left for Texas on a two-year deal that included an option for '14.
By signing Capps, the Twins lost out on receiving a compensation pick between the first and second rounds in the 2012 First-Year Player Draft. Capps was a modified Type B free agent, meaning the Twins didn't have to offer him arbitration to receive a Draft pick if he signed elsewhere.
Capps saved a career-high 42 games in 2010, including 16 with the Twins. He was acquired by Minnesota before the '10 Trade Deadline in a deal that sent catcher Wilson Ramos to the Nationals. Capps posted a 2.00 ERA in 27 innings with the Twins that season.
In a seven-year Major League career, Capps has 124 saves and a 3.51 ERA in 414 games for the Pirates, Nationals and Twins. Over the past five seasons, his ERA has fluctuated from 2.28, 3.02 and 2.47 in 2007, '08 and '10, respectively, 5.80 in '09 and 4.25 in '11.
"He had an off year," Ryan said. "I'm not trying to hide anything there. We just think he had an off year and we had a little bit of that last year. Relievers are like that a lot, and it's not just Matt. It happens many times."