Asche signed a minor-league contract with the Twins on Thursday.
Asche has not appeared in the majors since 2017, when he played in 19 games with the White Sox. The 29-year-old struggled in limited action at the Double-A level last season, recording a .655 OPS with one home run and 28 strikeouts over 23 games. Given Asche's past experience in the big leagues, it wouldn't be surprising if he's a non-roster invitee during spring training.