Paul McCartney, John Lennon, George Harrison, and original drummer Pete Best, signed the document on 24 January 1962, before achieving fame.
It gave Epstein responsibility for finding the band work, and managing their schedule and publicity.
The document was the first of two contracts drawn up between Epstein and The Beatles.
Gabriel Heaton, a specialist at Sotheby's auction house, which was in charge of the auction, said: "Epstein was just blown away by the passion, the energy, the charisma, the raw sexuality on stage."
"The Beatles had the stage energy but he instilled a sense of professionalism in them," Mr Heaton added.
"Epstein stopped them eating on stage, made sure they played the songs properly and coherently, and he got them bowing at the end of a set."
Source: BBC News