The Rangers on Monday announced the change in status for Greene, who on Jan. 21 signed a one-year, $750,000 deal with Texas.
General manager Jon Daniels issued a statement saying the Rangers fully support Greene's decision, and would not comment "on his medical situation." Daniels said the Rangers have not put a timetable on the 30-year-old player's possible return to the AL club.
Greene spent the 2009 season with St. Louis while missing 46 games in two stints on the disabled list due to social anxiety. Greene previously played for San Diego.
Texas on Wednesday will have its first full squad workout at spring training in Surprise, Ariz.