LSU made the announcement Monday night on its athletics website and Twitter. It said more details will be available Tuesday, but sources told ESPN's Jeff Goodman the deal is for six years.
The announcement was attributed to Vice Chancellor and athletic director Joe Alleva, who flew to Richmond on Sunday with deputy AD Eddie Nunez and met with Wade for several hours.
Wade, 34, was the head coach of the Rams for two seasons, taking over when Shaka Smart left for Texas in 2015.
VCU is 51-20 under Wade, making back-to-back NCAA tournament appearances.
Wade was also the head coach at Chattanooga for two seasons, going 40-25 overall and 27-7 in the Southern Conference.
Wade received an eight-year contract extension from VCU after his first season that called for him to make $1.4 million this season, plus incentives, and $1.5 million in each of the remaining seasons. LSU will have to pay the Rams $1 million as compensation for hiring Wade and agree to a home-and-home series with VCU within three years.
In a statement released Tuesday, VCU athletic director Ed McLaughlin said that during his annual end-of-the-season meeting with Wade: "Will and I agreed on the necessary next steps, and we met all of Will's requests. He ultimately decided he would rather coach elsewhere.''
The move comes at a difficult time for the Rams, who have reached the NCAA tournament for seven straight seasons. VCU and Kansas are the only teams that have won at least 24 games in each of the past 11 seasons, but because of that success, the Rams have lost four coaches to major college jobs since 2006.
The Rams will lose five graduating seniors from this year's team, including scoring leader JeQuan Lewis, and are slated to have only two seniors on next year's team. They were expected to be bolstered by a recruiting class ranked among the top 25 by several services that grade recruiting, but some of those recruits might now revisit those commitments.
McLaughlin is confident the VCU job will be attractive to candidates nonetheless.
"We have a world-class practice facility, a sold-out arena every night and one of the greatest fan bases in all of college basketball,'' he said. "VCU basketball is bigger than one person. We remain committed to ensuring that VCU basketball remains a top-25 program nationally. We have a tradition of remarkable success that is focused ultimately on providing our student-athletes with a positive experience, focusing on our core values: student-athlete focus, drive to excel and integrity.''
McLaughlin said a search for a successor begins immediately.
The Associated Press contributed to this report.