Godley, 25, was acquired by the D-backs in December in the trade that sent catcher Miguel Montero to the Cubs. Godley spent the first two seasons of his professional career as a reliever, but the D-backs have worked on converting him into a starter this season.
The right-hander was 8-3 with a 2.27 ERA in 14 games for Class A Advanced Visalia this year. He then made three starts for Mobile, going 1-1 with a 5.14 ERA.
While there were several candidates to make Thursday's start in the Minors, as well as long reliever Josh Collmenter, D-backs manager Chip Hale said the organization felt Godley was the best choice.