The White Sox released Kuhl on Tuesday, Daryl Van Schouwen of the Chicago Sun-Times reports.
The White Sox designated Kuhl for assignment Saturday.
Kuhl allowed a solo homer and struck out two batters while earning a save over the Astros on Friday.
Kuhl tossed 4.1 innings out of the bullpen in Thursday's 8-4 loss to the Guardians, striking out one batter while giving up three runs (two earned) on five hits and four walks.
Kuhl did not factor into the decision Thursday, allowing no runs on one hit and two walks over three innings against Atlanta. He struck out three.
Kuhl will start Thursday's game against Atlanta at Guaranteed Rate Field.
The White Sox selected Kuhl's contract from Triple-A Charlotte on Friday.
Kuhl signed a minor-league contract with the White Sox on Dec. 29.
Kuhl was released by the Nationals on Monday, Bobby Blanco of MASNSports.com reports.
The Nationals designated Kuhl for assignment Saturday, Jessica Camerato of MLB.com reports.