The 29-year-old Jones hasn’t pitched in the major leagues since April 3, 2014. He was recovering from Tommy John surgery performed July 29 of last year.
He is 12-5 with a 3.55 ERA in 137 relief appearances over three seasons.
In a corresponding move Wednesday, Chicago placed right-handed reliever Daniel Webb on the 15-day disabled list with a back strain. Webb is 1-0 with a 2.49 ERA in 17 relief appearances.