The "Sherlock" actor will star as Dominic Cummings, the strategist, who was the campaign director of the "Vote Leave" campaign.
Brexit, which is now the production's working title, is an utterly timely and compelling new political thriller from Olivier and RTS-winning screenwriter James Graham (Quiz, Ink, This House, The Vote, Tory Boyz, Coalition).
Directed by the award-winning Toby Haynes (Black Mirror, Jonathan Strange & Mr Norrell, Sherlock), the one-off drama is set primarily during the referendum.
Channel 4 said, "From political strategists and pollsters to disrupters and provocateurs - the decisions taken and platforms set out during those eight weeks in the summer of 2016 have had reverberations throughout British politics and across the globe like no other event since the fall of the Berlin Wall".
Brexit - which is a working title - will explore tactics used by campaigners in the controversial referendum on Britain's membership of the European Union.
"I'm so excited - not to mention a little nervous - to have this chance to try and get under the skin of what happened during that historic vote", added Graham.
Brexit is commissioned for Channel 4 by Beth Willis, Head of Drama. "And we're hugely excited that Toby Haynes will be directing this film for Channel 4". "We are so thrilled that he and the genius that is Benedict Cumberbatch feel Channel 4 is the right home for it - Brexit is exactly the kind of explosive and illuminating drama we want to have on the channel".
While the announcement is exciting, the show is pegged to begin filming via Lynn Horsford later on this year.