Carroll, 30, was 5-10 with a 4.80 ERA over 26 appearances (19 starts) last season, his first in the majors. He was designated for assignment on Nov. 25 to make room for first baseman Adam LaRoche on the 40-man roster.
The 25-year-old Snodgress spent most of last season in Chicago's minor-league system. He also debuted with the White Sox, allowing seven runs (four earned) in 2 1-3 innings over four relief appearances in September.
The moves announced Tuesday put Chicago's 40-man roster at 39.