Toby Haynes, whose credits include Black Mirror, will direct the one-off drama.
Brexit sets out not to be an analysis of who was right and who was wrong, but rather is the story of how it happened, and why.
Detailing the political strategists, pollsters, the decisions made and platforms set up and destroyed within the summer of 2016, Brexit promises to "go beyond the well-known public appearances of famous faces to peak behind the curtain".
While Graham said: "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". I hope by going behind-the-scenes of the campaign, we're able to interrogate the consequences of what happened during these eight weeks that have changed the country forever.
Brexit is commissioned for Channel 4 by Beth Willis, Head of Drama.
A new Channel 4 drama will have Benedict Cumberbatch portray the role of the leading strategist.
"James is a writer who is unafraid to ask hard questions and has never stopped looking for uncomfortable truths at this complicated time in our history". The drama will be directed by Toby Haynes and written by playwright James Graham.
The film will be produced by Lynn Horsford, with executive producers Juliette Howell and Tessa Ross for House Productions, and will begin shooting later this year.
The former Newsnight editor and Guardian deputy editor said he was committed to looking for diverse and new voices, while "doubling down on some of our shows which are more popular with younger viewers".