The deal is for three years and includes an option for a fourth and guarantees Hendriks $54 million, sources said.
Hendriks, 31, will make $39 million in the first three years, and the buyout and fourth-year option salary both are $15 million, sources said. If the White Sox decline the option, they will be able to pay the buyout over the course of multiple years.
Yahoo Sports first reported the agreement between Hendriks and the White Sox.
Hendriks, who became a free agent last month when the Oakland Athletics failed to make a qualifying offer, has been one of the most effective relievers in baseball over the past two seasons, ranking second in ERA (1.60), fourth in WHIP (0.87), third in strikeout ratio (7.2) and tied for eighth in saves (39).
He finished the 2020 regular season with a 1.78 ERA and an MLB-second-best 14 saves in 15 opportunities, and then recorded a win, a save and a 3.18 ERA in the postseason.
The Australian reliever established career bests with a 12.3 strikeout-walk ratio and 13.1 strikeouts per nine innings last season and was the Reliever of the Year in the American League.
Hendriks became a key piece for A's manager Bob Melvin late in games during the 2019 season. The right-hander, who earned $2.15 million in 2019, is the former opener who became a reliable closer. He went 4-4 with a 1.80 ERA and 25 saves over a career-high 75 appearances spanning 85 innings and made the All-Star team for the first time. He turns 32 on Feb. 10.
Hendriks was designated for assignment on June 25, 2018 -- he has been through that almost a half-dozen times now -- and then started Oakland's 7-2 wild-card loss at Yankee Stadium just more than three months later.
The Oakland closer received a nice raise when he signed a $5.3 million, one-year contract before the 2020 season to avoid salary arbitration.
In 10 major league seasons with the Twins, Royals, Blue Jays and A's, he has a 19-27 record with 40 saves and a 4.10 ERA.