Written by Ben Power, the film will be directed by Royal Court Theatre's former artistic director Dominic Cooke in his screen directing debut. Academy Award winner Sam Mendes ("American Beauty," Cabaret) will executive produce.
"I can't wait to work with Dominic Cooke again to bring this complex, funny and dangerous character to life," Cumberbatch told Deadline.com.
An Olivier Award winner, Cumberbatch's stage credits include the National Theatre's 2011 production of Frankenstein and 50 Years on Stage. He will star in Hamlet at the Barbican Theatre in August 2015.
Cumberbatch stars in the TV show "Sherlock," and his film credits include "August: Osage County," "The Fifth Estate" and "12 Years a Slave."