Finnegan signed a minor-league contract with the White Sox on Monday that includes an invite to major-league spring training.
Finnegan served as a non-roster invitee for the Reds in 2021 but spent the entire season at Triple-A Louisville. He made 40 appearances (one start) and logged a 5.53 ERA and 1.71 WHIP in 55.1 innings. The left-hander hasn't appeared in the majors since 2018 and appears likely to spent most of 2022 in the minors.