Snowden, who was granted temporary asylum by Russian authorities and now lives in Moscow, has previously spoken to Vanity Fair and appeared via Skype at South by Southwest last March.
NBC said Williams traveled to Moscow this week to speak to Snowden and Glenn Greenwald, the Guardian journalist who first published reports about Snowden's leaked NSA documents.
The hour-long interview will air Wednesday, May 28 at 10 p.m. ET.
Notable deaths of 2014 [PHOTOS]