Sources told ESPN.com on Wednesday that Rhoades would get a five-year deal. He will be introduced Thursday.
He takes over for Ben Braun, who resigned March 13 after Rice finished the season at 7-23.
Rhoades spent a decade at the helm at Division III Randolph-Macon College in Ashland, Va., and joined Shaka Smart's staff in 2009. The Rams went 137-46 during his five seasons as a VCU assistant and reached the Final Four in 2011.
Rhoades worked for three years as an assistant under Hal Nunnally, then took over in 1999 when Nunnally retired due to health issues. He was 197-76 in 10 years and made four Division III tournaments. Randolph-Macon went to the Sweet 16 in 2003.
The Associated Press contributed to this report.