Athletic director Jeff Compher said Monday that Godwin's contract will not be renewed.
Godwin was 317-215-1 with five NCAA tournament appearances at the school.
The Pirates were 33-26 this season, finished in a three-way tie for sixth place in the 13-team Conference USA and were not selected for the NCAA tournament. They will begin play in the American Athletic Conference next season.
The three-year extension he received after a Super Regional appearance in 2009 expires June 30.
Compher says the decision came "after a thorough and thoughtful evaluation."
He says he will conduct a national search for Godwin's replacement and appointed associate head coach Dan Roszel to run the program on an interim basis.