Jepsen was designated for assignment last week and went through waivers unclaimed.
The 31-year-old right-hander posted a 2-5 mark with a gaudy 6.16 ERA and 22 walks in 30 2/3 innings with Minnesota this season. He had four blown saves among 11 opportunities in 2016 in the wake of Glen Perkins' injury in April.
Acquired from Tampa Bay on July 31, Jepsen was far more successful for the Twins last season. He posted a 1-1 mark with a 1.61 ERA in 29 appearances, saving all but one of his 11 opportunities.