The Cubs sent Greene outright to Triple-A Iowa on Saturday, Paul Sullivan of the Chicago Tribune reports.
Greene was designated for assignment Wednesday in order to clear a roster spot for Luke Little, and he'll officially remain with the Cubs after clearing waivers. The 34-year-old righty holds a 2.16 ERA and 1.30 WHIP through 16.2 innings with Iowa this season, but he will likely finish the season in the minors now that he no longer has a spot on the 40-man roster.