Godley got the first look April 26 against the Padres and allowed two runs over five innings. Following the game, he was optioned back to Reno.
Braden Shipley was called up from Reno to start May 4 against the Nationals, and he gave up three runs and walked six in four innings. He also was optioned back to Reno.
Godley will get the start Wednesday because with Monday's off-day, that allows every pitcher in the rotation to get an extra day of rest this time through.
"I think he's been throwing the ball well enough to deserve this opportunity," D-backs manager Torey Lovullo said of Godley. "He came in and gave us five innings, gave us a chance to win the game his last start with us, and we want to see that continue."
Steve Gilbert has covered the D-backs for MLB.com since 2001. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.