The Twins reached agreement with Hughes last week and finished it on Thursday after the 27-year-old passed his physical. Hughes went 4-14 with a 5.19 ERA for the Yankees last season.
The Twins are hoping that a move out of hitter-friendly Yankee Stadium to spacious Target Field will help Hughes rediscover the promise he showed earlier in his career. Hughes was a first-round draft pick and an All-Star in 2010.
Twins starters had the worst ERA in baseball last season, so GM Terry Ryan has been aggressive in trying to upgrade the staff.
The Twins signed right-hander Ricky Nolasco to a $49 million, four-year contract Tuesday.