Cumberbatch will portray the enigmatic svengali in a new movie produced by Tom Hanks and his business partner Gary Goetzman.
Epstein was dubbed the "fifth Beatle" after leading the Beatles to international acclaim upon signing on to manage them in 1961.
He died in 1967 from an accidental overdose, amid reports of homosexuality and drug addiction.
Cumberbatch and McGuigan's Epstein biopic will rival another new project about the music manager - author Vivek J. Tiwary will write and produce an adaptation of his graphic novel about Epstein.
Tiwary has secured the rights to Beatles songs from Sony/ATV for his project.