Arizona also reinstated outfielder Cody Ross from the 15-day disabled list with a strained left calf.
Hudson has not pitched for Arizona since June 26, 2012, when he tore the ulnar collateral ligament in his right elbow against the Braves. Hudson was set to return in June 2013, but had a second Tommy John surgery after re-injuring his elbow.
Hudson had a 1.50 ERA in his rehabilitation appearances with Triple-A Reno and the Diamondbacks' rookie league team.
Ross hit .238 with two homers and 11 RBIs in 66 games this season in his return from a dislocated hip.