On January 4, 2018, Soria was traded to the Chicago White Sox in a three team trade that also sent Jake Peter and Scott Alexander to the Los Angeles Dodgers, Luis Avilán to the White Sox and Trevor Oaks and Erick Mejia to the Royals.
On July 26, 2018, Soria was traded to the Milwaukee Brewers in exchange for Kodi Medeiros and Wilber Pérez. Soria declined his half of a mutual option for 2019 and became a free agent, on October 30, 2018.
On December 21, 2018, Soria signed a two year contract with the Oakland Athletics. On June 25, 2019, Soria pitched in his 674th Major League game, passing Dennys Reyes for the most by a Mexican-born pitcher.