Nanne grew up in Ontario where he played hockey with Phil and Tony Esposito. In 1960, he enrolled at the University of Minnesota to play hockey for the Minnesota Gophers while studying business administration. At Minnesota, he would be coached by the legendary John Mariucci and would become one of the biggest stars in American college hockey during the 1960s. He is still the only defenseman to win the league scoring title which he accomplished in the 1962–63 season. In 1967, Nanne became an American citizen which allowed him to play for and captain the U.S. national team, alongside future Miracle on Ice coach Herb Brooks, which finished 6th at the 1968 Winter Olympics in Grenoble, France.