Stone, who won best director Oscars for "Platoon" and "Born on the Fourth of July," has written the screenplay based on two books - "The Snowden Files: The Inside Story of the World's Most Wanted Man" by Luke Harding and "Time of the Octopus" by Anatoly Kucherena.
The still untitled film goes into production in Munich in January, said independent studio Open Road Films and production and financing company Endgame Entertainment.
Producer Moritz Borman said in a statement that he and Stone chose Open Road and Endgame because "this film needs an independent in the true sense, where political pressures will not come into play."
Snowden leaked tens of thousands of classified intelligence documents to the media in 2013 and sparked a firestorm over the NSA's gathering of data from the Internet activities and phones of millions of ordinary Americans and dozens of world leaders.
The recently released documentary "Citizenfour" by Laura Poitras chronicles how the former NSA contractor decided to leak the documents and the global repercussions of that act.
Snowden spent almost six weeks at Moscow's Sheremetyevo airport before Russia granted him asylum for a year on Aug. 1, 2013, creating a furore in the United States. In August this year he was given a three-year resident permit by Russia and now lives at an undisclosed address in Moscow.
He is wanted by the United States on charges including theft of government property, unauthorized communication of national defense information and wilful communication of classified intelligence to an unauthorized person.
Gordon-Levitt, 33, most recently directed and starred in "Don Jon" and has acted in high-profile films "Lincoln," "The Dark Knight Rises" and "Inception."
© Thomson Reuters 2014