The 29-year-old right-hander was just 3-5 with a 6.39 ERA this season -- significant dips from a 2018 campaign that saw him go 15-11 with a 4.74 ERA. Most notably, Godley's strikeout rate has plummeted, going from 9.34 strikeouts per nine innings last year to 6.87 this season.
Godley was moved out of the regular starting rotation toward the end of April, but fared no better working out of the bullpen.
Godley, who is not eligible for arbitration until next winter, will now hit waivers.
In other moves Monday, Arizona recalled left-hander Robby Scott and selected righty Kevin Ginkel from Triple-A Reno.