Rhoades confirmed the move Tuesday, telling Fox 26 in Houston: "Dream come true. We're really excited about it. It's time to move forward and get going."
VCU has not officially announced the move but tweeted that it would introduce its new coach Wednesday.
Rhoades, 44, was an assistant coach under Shaka Smart at VCU for five seasons before spending the past three seasons at Rice. The Owls went 23-12 this season and advanced to the CBI before losing Monday to Utah Valley.
"Thank you for everything," Rhoades told Fox 26, referring to Rice and its fans. "Our family and I are going to really miss it."
Rhoades spent 13 seasons at Randolph-Macon, the final 10 as head coach. He made four Division III NCAA tournaments in those 10 seasons.
Rhoades replaces Wade, who was hired as the head coach at LSU on Monday. Both were finalists for the VCU opening after Smart left for Texas in 2015.