Dickey just completed the fourth season of a five-year contract with Houston. He coached Texas Tech from 1991-2001, and replaced Tom Penders at Houston in 2010. Dickey has a career record of 217-196.
He says in a statement it was a difficult decision, but did not give details as to why.
The Cougars went 17-16 this season with an 8-10 record in the American Athletic Conference. They also beat three Top 25 teams.
The Cougars' only postseason appearance under Dickey came in 2013 in the CBI.
Athletic director Mark Rhoades says Dickey's "decision to step down comes with great heartache for all involved."