The BBC Two production comes from the same team as the award-winning Hollow Crown series and will be directed by Dominic Cooke.
Cumberbatch said he "can't wait... to bring this complex, funny and dangerous character to life for the BBC".
His Sherlock co-star Martin Freeman will play the same role in London's West End later this year.
Freeman, who plays Dr John Watson in the BBC One drama, will take to the stage at Trafalgar Studios in the play, directed by Jamie Lloyd, .
Lloyd directed the theatre's production of Macbeth last year, starring James McAvoy.
BBC Two's new adaptation of the Shakespeare play will also mark the TV debut of director Cooke - a former artistic director of the Royal Court theatre.
Executive producer, Pippa Harris, said: "Neal Street Productions worked with Benedict on both Stuart: A Life Backwards for the BBC and the film Starter For Ten. His range and dexterity as an actor make him the perfect choice to bring one of Shakespeare's towering characters to television."
Ben Stephenson, the controller BBC Drama, described Cumberbatch as "one of the world's most brilliant and in-demand actors".
The 37-year-old will also star in William Shakespeare's classic tragedy Hamlet at London's Barbican Theatre in August next year.
Sherlock star Benedict Cumberbatch will play Richard III in the BBC's second series of Shakespeare's History plays.