Garton signed a minor-league contract with the Twins on Tuesday, Andersen Pickard of MLBDailyDish.com reports.
Garton is expected to receive an invitation to big-league camp as part of the deal. The 29-year-old isn't particularly likely to make the Opening Day roster, as he owns a career 4.90 ERA in 64.1 major-league innings, only three of which have come in the last two seasons.