The contract includes an option that could take the deal to a second year at $12 million total.
Cishek, a sidearming right-hander, played for the Chicago Cubs for the last two seasons on a two-year, $13 million contract.
In 2019, he made 70 appearances over 64 innings, with seven saves, a 4-6 record and an 2.95 ERA. Cishek, 33, also spent time on the disabled list with left hip inflammation.
The White Sox, looking to challenge in the AL Central in 2020, have been busy in free agency, adding catcher Yasmani Grandal ($73 million, four years), slugger Edwin Encarnacion ($12 million, one year) and pitchers Dallas Keuchel ($55.5 million, three years) and Gio Gonzalez ($5 million, one year). They also brought back slugger Jose Abreu on a $50 million, three-year deal.