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.
Kuhl (0-3) took the loss Sunday against the Royals after allowing two runs (one earned) on three hits while striking out two over 1.2 innings of work.
Kuhl gave up a hit and struck out two over 1.2 scoreless innings Friday to record his first save of the season in a 12-10 win over the Royals.
Kuhl (foot) was activated off the 15-day injured list Saturday but will pitch out of the bullpen for now, Jesse Dougherty of The Washington Post reports.
Kuhl (foot) threw a 65-pitch simulated game Monday, Jesse Dougherty of The Washington Post reports.
Kuhl (foot) threw 60 pitches in a three-inning simulated game Tuesday, Andrew Golden of The Washington Post reports.
The Nationals placed Kuhl on the 15-day injured list Monday with right foot metatarsalgia.
Kuhl will have his next start pushed back to Saturday's doubleheader after Friday's matchup with the Pirates was postponed, Jessica Camerato of MLB.com reports.