Kivlehan agreed to a contract with the Yakult Swallows of Nippon Professional Baseball in Japan on Thursday, Jon Heyman of MLB Network reports.
Kivlehan signed a minor-league contract with the White Sox on Friday.
Kivlehan was optioned to Triple-A El Paso on Monday.
The Padres selected Kivlehan's contract from Triple-A El Paso ahead of Wednesday's doubleheader with the Rockies.
The Padres reassigned Kivlehan to minor-league camp Wednesday.
Kivlehan signed a minor-league contract with the Padres on Sunday that includes an invitation to major-league spring training, Kevin Acee of The San Diego Union-Tribune reports.
Kivlehan was released by the Blue Jays on Tuesday, Andersen Pickard of MLBDailyDish.com reports.
The Blue Jays added Kivlehan to their 60-man roster pool Thursday.
Kivlehan signed a minor-league deal to remain with Toronto on Monday.
Kivlehan was traded from the Pirates to the Blue Jays on Friday for an undisclosed return.