Chicago also exercised a $4.65 million team option on reliever Nate Jones and reinstated right-hander Michael Kopech from the 60-day disabled list Monday.
Shields was 7-16 with a 4.53 ERA in 34 appearances -- 33 starts -- last season. He had a 5.31 ERA in two-plus years with the White Sox, who acquired him from San Diego for prospect Fernando Tatis Jr.
Jones was limited to 33 appearances by a strained muscle in his right arm.
Kopech had Tommy John surgery in September after making four starts for the White Sox and will miss next season.