"He'll eat up innings for us," said Twins Manager Ron Gardenhire. "Our bullpen worked a lot of innings in the first week of the season."
Mulholland was 3-4 with a 4.91 ERA with the Cleveland Indians in 2003. He allowed just five of 28 inherited runners to score and his 81 1/3 innings ranked ninth among relievers in the American League.
A 17-year veteran, Mulholland has a lifetime record of 119-131 with a 4.37 ERA.
The Twins designated lefthander Brad Thomas for assignment to make room for Mulholland.