Epstein, who discovered and signed the band in 1961, was a closeted homosexual who suffered from drug and gambling addictions and died of an accidental overdose in 1967.
The 36-year-old actor will work alongside his Sherlock director Paul McGuigan in the film.
Tom Hanks and Gary Goetzman are producing the project under their Playtone banner along with Simon Halfon. UTA are arranging the financing and will represent the movie for sale.
The producers said of the film: “It is the story of the man who threw the biggest party of the 1960s but ultimately forgot to invite himself.”
Cumberbatch can next be seen portraying Smaug the Dragon through voice and motion capture performance in Peter Jackson’s The Hobbit. He will also portray the antagonist in J. J. Abrams’ Star Trek Into Darkness, which is scheduled to be released in May 2013, and has recently signed on to play Daniel Craig’s next villain in the next instalment of the Bond franchise.
The casting news comes as more details on another film about the music manager have been released. Author Vivek J. Tiwary is writing and producing an adaptation of his graphic novel The Fifth Beatle.
The protect has secured the rights to include Beatles songs from Sony/ATV, which controls the John Lennon/Sir Paul McCartney music catalogue.