The move to axe three senior professionals will reduce the average age of the squad. Spurs have already secured the long-term futures of young stars Simon Davies and Ledley King, as well as having signed Jermain Defoe.
But Anderton, Gus Poyet and Christian Ziege have all been released, along with three reserves.
Levy said: "We wish Darren well. Gus and Christian have given the fans much to cheer about during their stay, too."
Anderton could now be targeted by former club Portsmouth, while Ziege has not been the same player since he sustained a horror thigh injury last season which required surgery to save his leg from amputation. Former Chelsea player Poyet is set to continue his career in Qatar.