The property, which has also been adapted into an opera by Philip Glass and Christopher Hampton, tells the story of a magistrate working in a small colonial town under threat of an attack by so-called "barbarians."
Rylance will play the role of the magistrate in the Ciro Guerra-helmed screen adaptation.
The actor was recently seen on Broadway in the West End transfer of Claire van Kampen’s Farinelli and the King, for which he received a Tony nomination. Prior to that production, he appeared on Broadway 2013 in Twelfth Night and Richard III, both of which transferred from the West End and played in repertory at the Belasco Theatre. His performance as Olivia in Twelfth Night won him a Tony for Featured Actor in a Play; he also won Tony Awards for his performances in Boeing-Boeing and Jerusalem.