Bruney would earn $600,000 if he makes the big league team. The White Sox have yet to confirm the deal.
Bruney pitched well for the White Sox last season before a string of poor outings that led to him being designated for assignment.
At one point he had a 2.16 ERA in 19 outings before giving up 11 runs over his next three innings. His departure paved the way for Zach Stewart to join the major league roster.
Bruney was said to be working through injury issues at the time he was struggling and expressed a desire to return to the White Sox if the feeling was mutual.