Van Gundy had an option year remaining on his current contract but team management and the coach were unable to come to terms on a new deal, the Rockets said. He was offered a "senior consultant capacity" slot with the organization but turned that down.
Rockets General Manager Daryl Morey thanked Van Gundy but said during conversations about the coach's future with the team "it became clear that Jeff did not want to continue in any capacity with the team other than as head coach."
Houston was 182-146 over four seasons under Van Gundy. The team made the playoffs in 2004, 2005 and 2007. The Rockets lost to the Utah Jazz in seven games in this year's playoffs.
Van Gundy, who previously coached the New York Knicks, has an overall coaching record of 430-318.
Campus cop fatally shoots Texas student during traffic stop
Newt Gingrich fires back at Mandela backlash