Despaigne signed a one-year, $800,000 contract with the Korea Baseball Organization's KT Wiz on Wednesday, the Yonhap News Agency reports.
Despaigne was designated for assignment by the White Sox on Monday.
Despaigne allowed four runs on eight hits and one walk over three-plus innings in a no-decision Saturday against the Rangers.
Despaigne (0-2) gave up seven runs on nine hits and four walks while striking out five through 4.1 innings, taking the loss against the Yankees on Sunday.
Despaigne is listed as the White Sox's probable starter for Sunday's game against the Yankees.
Despaigne had his contract purchased from Triple-A Charlotte ahead of his scheduled start against the Nationals on Monday.
Despaigne is expected to have his contract selected from Triple-A Charlotte to start Monday's game against the Nationals, Daryl Van Schouwen of the Chicago Sun-Times reports.
Despaigne signed a minor-league contract with the White Sox on Sunday and was assigned to Triple-A Charlotte, Daryl Van Schouwen of the Chicago Sun-Times reports.
Despaigne was reassigned to minor-league camp Tuesday, Bobby Nightengale of The Cincinnati Enquirer reports.
Despaigne signed a minor-league contract with the Reds on Tuesday, Ben Nicholson-Smith of Sportsnet.ca reports.