San Francisco sent right-handed reliever Sam Dyson to the Twins and kept 2014 World Series MVP Madison Bumgarner.
Twins got Dyson in exchange for outfielder Jaylin Davis and right-handed pitchers Prelander Berroa and Kai-Wei Teng.
The 31-year-old right hander appeared in 49 games for the Giants this season, going 4-1 with a 2.47 ERA (51.0 IP, 14 ER), two saves, 17 holds, seven walks, 47 strikeouts, a WHIP of 0.90 and an opponent batting average of .213.
Dyson has appeared in 364 career major league games in parts of eight seasons with Toronto, Miami, Texas and San Francisco, going 23-23 with a 3.29 ERA (375.1 IP, 137 ER), 59 saves, 123 walks and 302 strikeouts, according a news release from the Twins.