Green was signed by the White Sox and assigned to Triple-A Charlotte on Wednesday, Daryl Van Schouwen of the Chicago Sun-Times reports.
Green was released by the Nationals last week after appearing in 40 games with Triple-A Syracuse this season, where he slashed .246/.319/.285, but failed to make much of an impact on his overall stock. Over 129 career games with the A's, Angels, Giants and Nationals, the 29-year-old has compiled a .246 average and 38 RBI while mainly being used as a reserve infielder. He'll serve as organizational depth for a White Sox team already dealing with injuries to Tyler Saladino and Leury Garcia, but remains a longshot to see much, if any, major-league playing time.