Altavilla signed a minor-league contract with the Twins on Wednesday, Francys Romero of BeisbolFR.com reports.
Altavilla posted a 2.48 ERA and 1.17 WHIP over 29 innings with the White Sox this past season, but his 5.44 FIP indicates that his performance wasn't quite as impressive as the basic stats might suggest. That being said, the Twins' lack of reliever depth greatly improves the 33-year-old's chances of winning a spot in Minnesota's Opening Day bullpen.