Johnson signed a 2022 minor-league contract with the White Sox on Tuesday, Daryl Van Schouwen of the Chicago Sun-Times reports.
Johnson was released by the White Sox on Thursday.
Johnson's contract was purchased by the White Sox on Friday.
The White Sox announced Monday that Johnson will be included as part of the team's 60-man roster pool.
Johnson's (lat) rehab assignment has been transferred to High-A Winston-Salem, James Fegan of The Athletic reports.
Johnson (lat strain) is on the 7-day IL at Double-A Birmingham, Jim Callis of MLB.com reports.