Sources said the deal is worth almost $18 million.
"We sincerely appreciate the contributions Buzz has made to Marquette University, both on and off the courtk," athletic director Bill Cords said in a statement Friday. "During his six-year tenure, he helped elevate the program to one of the most successful in the Big East Conference. We wish him and his family nothing but the best in the future."
The 41-year-old Williams led the Golden Eagles to five NCAA tournament berths in six seasons since taking over after Tom Crean left for Indiana.
He was 139-65 at Marquette and took the team to the Elite Eight in 2013 as well as the Sweet 16 in 2011 and 2012.
Cords said that Marquette has already started its search for a new coach and that "we look forward to finding the right person who will make us stronger in the future."
Williams replaces James Johnson, who won just 22 games in two seasons after being tabbed to replace Seth Greenberg.
Johnson was fired this month by new athletic director Whit Babcock.