The 60-year-old Braun compiled a 63-128 record in six seasons at Rice and has an overall record of 615-517 as a college coach. The Owls went 7-23 this past season, which finished with a 63-62 overtime loss to North Texas in Tuesday's opening round of the Conference USA Tournament.
"Ben and I met this morning to review the program and at that time he expressed to me his decision to resign as our head coach," Rice athletics director Joe Karlgaard said. "I want to thank Ben for his hard work during his time at Rice. We will immediately begin identifying and contacting individuals who we feel are ready to come to Rice and lead this program to an exciting future."
Over his 36 years of coaching, Braun has led teams to seven NCAA Tournament appearances, including two trips to the Sweet 16. He previously spent 11 seasons as the head coach at Eastern Michigan (1985-96) and 12 years at California (1996-2008). The Golden Bears were NIT champions in 1999.
The top season for Braun at Rice came in 2011-12, when he led the Owls to a 19-16 record and a berth in the quarterfinals of the CollegeInsider.com tourney.