He insisted he has no retirement plans, saying it was simply time to find another challenge.
"I came to the University of Houston in 2004 with the goal of getting UH back to the NCAA tournament," he said. "We achieved this goal and now it is time for me to move on."
The 64-year-old Penders became just the eighth coach to take four different schools to the NCAA tournament. He had also led George Washington, Rhode Island and Texas there.
Penders has won 648 games in his more than 30-year head coaching career. He went 121-77 at Houston.
Penders has spent the majority of his career turning around struggling programs, including those at Tufts, Columbia, Fordham and Rhode Island. He took great pleasure in leading the once-proud Houston program back to the tournament for the first time in almost two decades.
"We'll go down in history as the team that brought UH back to national prominence, and I'm so proud of my players and staff," he said.
He became the first coach in school history to lead the team to at least 18 wins in six straight years and the fourth coach to take the Cougars to the NCAA tournament.
In a Monday morning meeting with his team, he told the players they were the "most special group" he's ever coached.
"This was different," he said. "This was a challenge, a real challenge because of some of the things that we don't have. But I love challenges."
Penders came to Houston after a three-year break from coaching during which he worked as a radio and television analyst. Before that he spent 1998-2001 at George Washington, where he landed after 10 seasons at Texas in which the Longhorns reached the NCAA tournament eight times.
Both he and athletic director Mack Rhoades emphasized that the parting, which comes with two years left on his contract, was Penders' decision.
"He certainly initiated the opportunity to resign," Rhoades said. "We will work with Tom to negotiate a fair exit. That's what he deserves."
Rhoades, who was hired last June, was impressed with what Penders did with the limited resources he had at Houston.
"Tom did a great job," Rhoades said. "This is a hard job because there are a lot of things that other schools have that you don't. He did a terrific job of moving that needle forward and now it's my job, our job with the next head coach to move that even further."
Rhoades said he has not contacted anyone concerning the opening, but that he would begin the process Monday afternoon. Some have already speculated that he's eyeing former Kentucky and Texas A&M coach Billy Gillispie, with whom he worked at UTEP. Rhoades said he doesn't know if he'll be a candidate, but that it is a possibility.