The White Sox officially announced the move on Monday.
Rodon, who was selected by the White Sox with the No. 3 overall pick in the 2014 amateur draft, became a free agent after he was not tendered a contract after the 2020 season.
He broke into the majors in 2015 and looked as if he could be a key member of the team's rotation for years to come before he was hampered by a series of injuries.
Rodon, 28, is 29-33 with a 4.14 ERA in 97 career major league games, including 92 starts. He made four appearances last season, going 0-2 with an 8.22 ERA.
The Associated Press contributed to this report.