"We like what we see," Gibson said. "We rearranged our pitching the other day and talked about everybody, where they are with their innings, etc. We just went through, 'Why have him go on?' He has accomplished everything we wanted him to accomplish this year."
Hudson pitched an inning in relief against the Padres on Sept. 3, his first big league appearance since June 26, 2012, when he tore his ulnar collateral ligament.
A starter in his career before the injuries, Hudson figures to be part of the Arizona bullpen next season. His velocity touched 96 mph during his outings this month, and he could wind up pitching in late-inning situations next year.
"He threw the ball well," Gibson said. "He got ready for us pretty good in the bullpen. He had three here and probably six to seven prior to that in the Minor Leagues. He got to throw quite a bit. His velocity is good. His arm action is good."
Hudson allowed four runs in 2 2/3 innings over his three appearances.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.