Soria, 34, had an 18.00 ERA without a decision in two innings over four appearances in the National League Championship Series against the Dodgers. He was 1-0 and allowed just one hit and no runs in 2 2/3 innings in the division series sweep over the Rockies, appearing in all three games.
Before his move to Milwaukee, Soria had emerged as Chicago's closer, compiling 16 saves last season. He had a 0.74 ERA with 32 strikeouts over his last 23 games dating to May 21. The White Sox had acquired the veteran reliever from the Kansas City Royals as part of a three-team trade in January.
Soria had 42 saves for the Royals in 2008 and 43 more in 2010. He compiled 160 over a five-year stretch before needing a second Tommy John surgery in 2012. He left the Royals and collected 44 additional saves in four years with Texas, Detroit and Pittsburgh before returning to Kansas City in the 2016 season.
Soria, an All-Star in two of his first four seasons with the Royals, has 220 career saves and 688 strikeouts in 639 games since entering the majors in 2007.