The actor will reunite with Sherlock director Paul McGuigan on the currently untitled film, which will focus on Epstein himself rather than the band, according to The Hollywood Reporter.
Epstein - often referred to as "the fifth Beatle" - signed the band in 1961, and died six years later from an accidental overdose, having struggled with gambling, drug addictions and his sexuality.
The project has been described by producers Tom Hanks and Gary Goetzman as the story of "the man who threw the biggest party of the 1960s, but ultimately forgot to invite himself".
Todd Graff (Joyful Noise, Bandslam) penned the script.
McGuigan has directed four of Sherlock's six episodes to date, including the Emmy-nominated 'A Scandal in Belgravia'.
> Benedict Cumberbatch to play Julian Assange in biopic?
> Benedict Cumberbatch on 'Parade's End': "My look suits a period drama"
Watch Cumberbatch discussing Sherlock with Digital Spy below: