The hire represents another big step in Miami's commitment to revamping its leadership after hiring former Hurricanes player Mario Cristobal away from Oregon as the new football coach.
"I am so grateful to President [Julio] Frenk and the University's Board of Trustees for this incredible opportunity," Radakovich said in a statement. "Their commitment to Miami Athletics' comprehensive pursuit of excellence and championships is what brought me back to Miami. As a unified Hurricane family -- students, alumni, donors, and fans -- there is nothing that we cannot accomplish. We are going to set the bar high and jump over it."
Radakovich has served as athletic director at Clemson since 2012, overseeing a massive expansion in the program's budget while the team played for the national title in football four times, winning two.
The Miami deal is expected to make Radakovich among the highest-paid athletic directors in the nation.
Clemson has elevated deputy athletic director Graham Neff to acting athletic director, the school announced. Neff, who worked under Radakovich at Clemson and Georgia Tech, is widely expected to take over permanently at Clemson.
Radakovich, 63, will replace Blake James, whom Miami let go last month, two days after the Hurricanes' football team lost to Florida State.
With Radakovich, the Hurricanes are bringing another alum back to Coral Gables. He got a master's degree in business administration from Miami in 1982.
Miami becomes the third ACC school to have Radakovich as athletic director. Before his stint at Clemson, he was at Georgia Tech from 2006 through 2012.
"Everybody that I've spoken to that knows Dan raves about him," Miami men's basketball coach Jim Larranaga said earlier this month as it was becoming clear that Radakovich was the Hurricanes' top target for the job.
Larranaga added: "He's a heck of a businessman. He's got tremendous experience."
Radakovich's career in sports administration began in 1983 at Miami, so his hiring by the Hurricanes has his career coming full circle.
Radakovich, then 25, left an accounting firm to take a job working for legendary Miami athletic director Sam Jankovich as the Hurricanes' director of athletic financial affairs. He arrived about 2½ months before the football team won its first national championship.
His task now is to help Miami get back to that level.
The Associated Press contributed to this report.