Washington State director of athletics Jim Sterk confirmed that Bennett has accepted the head-coaching position at Virginia on Tuesday.
"Dick and Tony Bennett have elevated the men's basketball program at Washington State to an unprecedented level of success," Sterk said in a statement released by the university. "We will begin a national search for a coach immediately with the goal of finding someone with the integrity, experience, and values that Dick and Tony brought to the program."
Bennett, who led the Cougars to consecutive NCAA tournament appearances before finishing 17-16 this past season, replaces former Cavaliers coach Dave Leitao, who resigned March 16.
Financial terms of Bennett's contract with Virginia weren't immediately known.
Sterk said that Virginia asked for permission to speak with Bennett last Friday. Monday afternoon Bennett informed Sterk and WSU president Elson S. Floyd of his decision to accept the position at Virginia. Following those conversations, Bennett informed his players of his decision.
"I was so shocked," freshman guard Klay Thompson told the Spokesman-Review in Spokane, Wash. "I'm disappointed, I'm really disappointed. Shoot, I don't know. But it's life. I'll adjust."
Virginia officials planned an official announcement for Wednesday.
Bennett, 38, played for his father, Dick, at Wisconsin-Green Bay, where he finished as the Mid-Continent Conference's all-time leader in points (2,285) and assists (601). He still ranks as the NCAA's all-time leader in 3-point percentage (.497). He served on his father's staff as an assistant at Wisconsin and later at Washington State.
Bennett was named his father's successor and led the Cougars to their first NCAA tournament appearance since 1994 in his first season in 2006-07, as Washington State lost to Vanderbilt in double overtime in the second round of the NCAA tournament. He was named the AP college basketball coach of the year in 2007.
The next season, the Cougars advanced to the Sweet 16 before losing to a team Bennett will face regularly in the Atlantic Coast Conference -- North Carolina. This year's squad was eliminated in the first round of the NIT.
Last year, he declined interest for LSU and Indiana openings to stay at Washington State.
Virginia finished 10-18 this past season, its worst finish since 1967-68. Leitao had a 63-60 record in four seasons.
Mark Schlabach covers college basketball and college football for ESPN.com. Information from The Associated Press was used in this report.