Greene signed a minor-league contract with the Astros on Feb. 23, Kenny Van Doren of MLB Pipeline reports.
The Orioles released Greene on Tuesday, Andy Kostka of The Baltimore Sun reports.
Greene was reassigned to minor-league spring training Wednesday, Nathan Ruiz of The Baltimore Sun reports.
Greene signed a contract with the Orioles on Monday, which includes an invitation to spring training, Robert Murray of FanSided.com reports.
Greene elected free agency after being outrighted to Triple-A by Baltimore on Friday, Rich Dubroff of BaltimoreBaseball.com reports.
Greene was outrighted to Triple-A Norfolk by the Orioles on Wednesday, Roch Kubatko of MASNSports.com reports.
Greene (1-2) allowed two runs on three hits and a walk in two-thirds of an inning, taking the loss Wednesday versus Philadelphia.
Greene pitched a scoreless first inning, giving up one hit while striking out two in the loss to the Phillies on Monday.
Greene will be the first pitcher on the mound for Tuesday's bullpen game against the Phillies, Dan Connolly of The Athletic reports.
Greene (1-1) allowed three runs on three hits in one-third of an inning, taking the loss Sunday versus Boston.