Jones chose the Cardinals over a final list that included Maryland and Michigan State, among others.
Jones made the announcement via Instagram.
Jones, a 6-foot-1 guard from Cincinnati, emerged as the No. 1 graduate transfer in the country after entering the transfer portal in late March. The Big South Player of the Year averaged 20.0 points, 5.1 rebounds and 5.5 assists last season, shooting 40.9% from 3-point range.
He was a first-team All-Big South selection in 2018-19 after putting up 15.7 points and 5.8 assists.
Jones helped lead Radford to the NCAA tournament in 2018 and back-to-back Big South regular-season championships in 2019 and 2020. He scored 33 points in a Big South tournament loss to Hampton in his final game earlier this month.
Jones should start immediately next season for Chris Mack and Louisville, as the Cardinals lose seniors Lamarr Kimble, Ryan McMahon, Dwayne Sutton and Steven Enoch and are expected to lose All-American forward Jordan Nwora to the NBA draft. Top junior college prospect Jay Scrubb, a Louisville signee, also announced last month that he would test the NBA draft process.