The EIFF Audience Award at the festival, which closed at the weekend, went to the film made by director and producer Skip Kite.
Skip Kite said: "Praslin Pictures, and everyone involved in the making of the film, are truly honoured that Will & Testament has been so wonderfully received by the Edinburgh International Film Festival audience.
"We are very proud to have launched the film here and our heartfelt thanks goes to all the festival staff and everyone involved with the world premiere.
"We know that Tony would have been absolutely delighted and humbled, and we are too."
Benn, an MP for 47 years, died on March 14 this year.
Chris Fujiwara, who is artistic director of the film festival, added: "Our audience's decision reflects both the enduring significance of Tony Benn himself and the force and conviction with which the film pays tribute to him.
"The film is a rousing argument for compassionate politics, and this award shows how well that argument communicated to our audience."
lA sequel to the controversial documentary about Donald Trump's contentious golf resort in Aberdeenshire is to be released later this year.
Anthony Baxter's A Dangerous Game, made by Anthony Baxter, features heavy criticism of Alex Salmond, and his support for the development.
Mr Baxter has been unable to secure any interviews with Mr Salmond for the making of the film,