Alston was in the final year of a contract that was to pay him $5.25 million this season. The two sides did not disclose the buyout payment.
Alston averaged 9.7 points and 3.9 assists in 27 games, including 13 starts.
Nets coach and general manager Kiki Vandeweghe said that Alston was a consummate professional in a season that opened with an NBA-record 18 straight losses.
"To me he was clearly in a situation that was tough for him," Vandeweghe said. "He's been a star, a starter for most of his career and played in the championship series last year, and has a lot more basketball in him. To be able to set up a situation where he potentially can get to a place where he wants to go and out of a situation that is not good for him is, I think, is clearly good for everybody."
Vandeweghe said that Alston never complained and only recently came to him to discuss a buyout.
Dan Fegan, Alston's agent, did not immediately return a telephone call from The Associated Press seeking comment.
The Nets acquired Alston, shooting guard Courtney Lee and power forward Tony Battie from Orlando in a draft-day trade that sent eight-time All-Star guard Vince Carter and forward Ryan Anderson to the Magic.