Terms of the deal, which was announced Thursday, were not disclosed.
Nelson, 32, ended a 10-year run as the Magic's all-time leader in assists and second in team history in games played.
The Magic saved a reported $6 million by waiving Nelson, who had re-signed with the team on a three-year deal in July 2012 amid swirling speculation about Dwight Howard's future with the team.
Nelson posted 12.1 points and 7.0 assists in 68 games this past season and has averaged 12.6 points and 5.4 assists in his NBA career. He made it to the NBA Finals with the Magic in 2009, the same year he was an All-Star for the only time.
The former Naismith Award winner was selected by Denver in the first round of the 2004 draft out of Saint Joseph's but traded to Orlando on draft night for a future first-round pick.
As a senior in 2004, he led Saint Joseph's to an undefeated regular season, a No. 1 national ranking and into the regional final of the NCAA Tournament, drawing widespread attention for the Philadelphia school and landing him on the cover of Sports Illustrated.