Slowey, 27, went 0-8 with a 6.67 ERA in 59 1/3 innings last season. He started the year in the bullpen but battled forearm issues and an abdominal strain, and finished the season in the starting rotation.
Slowey, though, struggled as a starter, going 0-8 with a 7.25 ERA in eight outings down the stretch. Because of his struggles, Slowey, who made $2.7 million last season, was a non-tender candidate for the Twins.
"I think it's probably good for Kevin," Twins general manager Terry Ryan said. "I think sometimes a change of scenery is probably beneficial. It's as simple as that. There's nothing more, nothing less to it. I explained that to him this morning."
Ryan wouldn't indicate when the Twins will receive the player to be named, but the player isn't expected to come from the Rockies' 40-man roster.
Slowey fared much better as a starter in 2010, going 13-6 with a 4.45 ERA in 30 games (28 starts) totaling 155 2/3 innings. The right-hander has a career 4.66 ERA with 395 strikeouts, 84 walks and 84 homers allowed in 532 2/3 innings.
A strike-throwing, fly-ball pitcher, Slowey's 4.70 strikeout-to-walk ratio ranks third among Major League starters behind Roy Halladay (5.30) and Cliff Lee (4.86) since coming into the league in '07. But over that same span, his 1.42 home runs allowed per nine innings ranks as the second-highest among starters behind Armando Galarraga (1.53).
His struggles were apparent last season, when he went 0-8 in eight starts to become the first Major League pitcher in 60 years to make at least eight starts in a season and lose each one. The last to do it was Lou Sleater in 1951 with the St. Louis Browns, according to STATS LLC.
"He just had a difficult year, but so did the club," Ryan said. "He had a difficult year, but there were a lot of things that didn't go well last year. But I don't know why things didn't go so well for him. There was talk about being in the bullpen versus starting and then he got hurt. So there are some things there that complicated matters."