Wright signed a minor-league contract with the White Sox on Sunday and was assigned to Triple-A Charlotte.
Wright signed with the Dodgers as a non-roster invitee Monday, Fabian Ardaya of The Athletic reports.
Wright was designated for assignment by the White Sox on Friday, Daryl Van Schouwen of the Chicago Sun-Times reports.
The White Sox reinstated Wright (suspension) on Sunday.
Wright had his suspension for intentionally throwing at Shohei Ohtani reduced to two games and will begin serving the ban Friday at Cleveland, James Fegan of The Athletic reports.
Wright was handed a three-game suspension Saturday for intentionally throwing at Shohei Ohtani on Thursday, but he's elected to appeal and won't begin serving the ban yet, Bob Nightengale of USA Today reports.
The White Sox selected Wright's contract from Triple-A Charlotte on Monday.
Wright will start Chicago's Cactus League opener against the Brewers on Sunday, Scott Merkin of MLB.com reports.
Wright joined the White Sox as a non-roster invitee Thursday.
Wright signed a contract with the NC Dinos of the Korean Baseball Organization on Friday, Dan Kurtz of MyKBO.net reports.