Jepsen, 31, figures to be the club's top setup reliever for closer Glen Perkins, as the Twins are looking to upgrade a bullpen that has posted a 3.97 ERA, which ranks 24th in the Majors.
Jepsen has a 2.81 ERA with 34 strikeouts and 20 walks in 41 2/3 innings with Tampa Bay this year. The eight-year veteran, who played with the Angels from 2008-14 before joining the Rays this season, has a career 3.80 ERA with 305 strikeouts and 130 walks in 322 1/3 innings.
He's a hard thrower, as his fastball averages 94.