Yahoo! Sports, CBS Sports and ESPN all have reported that Williams is headed to Virginia Tech.
Williams, 41, took over as head coach on April 7, 2008, after Tom Crean left MU to coach at Indiana University.
Marquette made the NCAA Men's Division I Basketball Tournament in Williams' first five years as head coach, and fell short of the tournament in the 2013-14 season. Marquette went to the Elite Eight in 2013 and to the Sweet 16 in 2011 and 2012.
Marquette University and athletic department officials could not be reached for comment, but the university's Twitter handle, @MarquetteU, confirmed that Buzz is leaving.
"We wish the best of luck to @TeamCoachBuzz. Thank you for the memories (and) all you've done for the Marquette family. #WeAreMarquette," Marquette stated in a Tweet.
Update: Marquette University issued the following statement:
“Head Men’s Basketball Coach Buzz Williams has been an integral part of the Marquette community for the past seven years, including six as head coach, and we wish him and his family all the best as he takes on this new opportunity. Coach Williams led the Marquette men’s basketball team to five-straight NCAA tournament appearances, including three-straight Sweet 16 appearances and an Elite Eight run last year. Coach Williams had a record of 139-65 during his six years at Marquette, including leading his team to a 2012-13 Big East Conference Championship. His commitment to player development and the creation of Buzz’s Bunch, which provides children with medical needs positivity and support, were the hallmarks of his success off the court. The university has already begun a search for a new head coach, and we are confident that we will attract top-tier talent. Marquette’s elite basketball program is built on a proud tradition of excellence and we look forward to continuing to build on that legacy.”