The script, which is based on a pitch by Matt Charman, was written by the Coen brothers.
The film will follow James Donovan, an American attorney enlisted by the CIA to slip behind the Iron Curtain during the Cold War in order to negotiate the release of a pilot captured when his U2 spy plane was shot down over Russia.
Details on Rylance's character have yet to be revealed.
Rylance won a 2014 Tony Award for Best Featured Actor in a Play for his performance in Shakespeare's Twelfth Night. He was also nominated for Best Leading Actor in a Play for the title role in Richard III. The Shakespeare's Globe productions were performed in repertory by an all-male cast wearing traditional Elizabethan costumes. Rylance also received Tony Awards for his performances in Boeing-Boeing and Jerusalem, respectively, in 2008 and 2011.
The film will begin production in the fall.