Sources said Williams' seven-year deal with Virginia Tech is worth almost $18 million.
"It's never easy to leave a great school like Marquette, where I spent seven wonderful years, six as the head coach," Williams said in a statement released by Virginia Tech. "I've heard tremendous things about this terrific institution and this is an outstanding opportunity to build a program."
According to a source with direct knowledge of the negotiated deal, Williams took a pay cut to come to Virginia Tech and the ACC. Williams' first-year salary at Virginia Tech will be $2.3 million, according to the source, which will be significantly less than his $3 million annual salary at Marquette. Williams' buyout to leave Marquette was $100,000, according to the source.
His buyout to leave Marquette was only $100,000. The source said Williams made over $3 million a year at Marquette last year.
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.
"I am extremely excited about welcoming Buzz Williams to the Hokie Nation," new Virginia Tech athletic director Whit Babcock said in a statement. "Buzz is a proven winner who has earned his way up through the ranks with a strong track record of success.
"I am confident he will energize our fan base and help make Virginia Tech basketball competitive in the Atlantic Coast Conference. I know he will recruit at the highest level."
Williams was 139-65 at Marquette and took the team to the Elite Eight in 2013 as well as the Sweet 16 in 2011 and '12. After going 17-15 this season, the Golden Eagles' eight-year run of NCAA tournament appearances ended.
"We sincerely appreciate the contributions Buzz has made to Marquette University, both on and off the court," athletic director Bill Cords said in a statement. "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."
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 was fired this month by Babcock after winning just 22 games in two seasons since replacing Seth Greenberg.
ESPN.com's Andy Katz contributed to this report.