Citizenfour takes its title from an alias used by Mr Snowden, the National Security Agency (NSA) contractor who approached a journalist with his secrets last year, aged 29. Billed as a real-life thriller, it joins the renegade security analyst after he fled the US and arrived in Hong Kong.
It mixes comedy with suspense as the NSA operative tells his story to journalists from the Guardian newspaper and filmmaker Laura Poitras in a hotel room that becomes increasingly cluttered with computer hardware.
It also sheds light on the personal story of Mr Snowden and his decision to give up relationships with his girlfriend and family – possibly for ever.
But, above all, it outlines the way millions of people had their phones and digital communications intercepted.
Susan Sarandon, the campaigning actress, attended a screening yesterday, and said she hoped the film would play to big audience across the country so that no-one would forget how the NSA was prying into their lives.
“I just hope a lot of people see it,” she told The Scotsman. “It’s a really vivid telling of the story and I hope that it refreshes the conversation that started when he released all the information because it’s a very important conversation.”
The film covers Mr Snowden’s revelation that GCHQ, the UK listening station, goes far beyond what any US agency is allowed to do, collecting not just phone call details – metadata – and emails but also content.
The film closes with images of Mr Snowden in his Moscow home with his girlfriend, Lindsay Mills.
He spoke for the first time at the weekend about the huge strain he placed on their relationship when he went into hiding with no idea whether they would ever see each other again. He told his girlfriend he had gone on a work trip.
“She was not entirely pleased but at the same time it was an incredible reunion because she understood me. That meant a lot to me,” he said, via a videolink from Moscow to the New Yorker festival.
Mr Snowden remains a wanted man in the US under the Espionage Act. He said he would be happy to return to the US if he were guaranteed a fair trial and admitted missing home.
But he added that he had no regrets and had always known his work would mean making sacrifices.
For the time being, he said he was working on a grant from a foundation to protect journalists working in difficult environments, but said his backers would rather he did not reveal their identity.
He also offered advice on how ordinary citizens could avoid snoopers, by steering clear of websites such as Facebook and Google, which stored user information, ditching the cloud storage service Drop Box and adopting encryption apps for email and text messaging.
“We’re talking about encryption. We’re talking about dropping programs that are hostile to privacy,” he said.
The film will receive its British premiere at the BFI London Film Festival on Friday.