The Twins selected their contracts on Friday from Triple-A Rochester before playing at Cleveland. Left-hander Mason Melotakis and right-hander Alex Wimmers were designated for assignment.
Gee, 31, was signed to a minor league contract this week after Texas released him. He'll likely join the rotation, with rookie Nik Turley the latest starter sent back to Triple-A on Thursday. The Twins have no off days until the All-Star break and a doubleheader at Kansas City on July 1.
Gee worked out of both the bullpen and the rotation last season for the Royals, posting a 4.68 ERA in 125 innings. He made 110 starts with a 4.03 ERA over six years with the New York Mets, including a career-best 2013 season with 12 wins and a 3.62 ERA over 199 innings.
He gets a contract calling for a $1 million salary in the major leagues and $180,000 in the minors.
Hildenberger, 26, is a sidearmer with six saves with a 2.05 ERA and 35 strikeouts in 30 2/3 innings for Rochester. He gets the $535,000 minimum in the majors and $87,200 in the minors.
Wimmers, the team's first-round draft pick in 2010, has a 4.38 ERA over 22 appearances for the Twins while going up and down to the minors the last two seasons. He's 28.
Melotakis is a bigger risk to expose to waivers. He has 32 strikeouts with a 2.28 ERA in 27 2/3 innings this year between Double-A and Triple-A. The 2012 second-round draft pick turns 26 next week.