The 1962 document is said to be one of the most important contracts in popular music, marking the beginning of the band's journey to international fame.
The contract had been expected to fetch up to £500,000 in a sale of other rock memorabilia.
It last went under the hammer in 2008 at an auction in London when it went for £240,000.
It is the only managerial contract signed by both the final line-up of the Beatles - John Lennon, Paul McCartney, George Harrison and Ringo Starr - and their manager.
The contract was signed on 1 October 1962 at Epstein's office in Whitechapel, days before they released their first single, Love Me Do. It was witnessed by Epstein's secretary, Beryl Adams.
A single page from John Lennon's high school's detention book was also sold for £2,500, recording 29 occasions when he received detention at Quarry Bank High School in Allerton, Liverpool.
£1.75m Rolls Royce Phantom V belonging to John Lennon
£1.45m The piano on which John Lennon wrote Imagine
£800k Handwritten lyrics for A Day in the Life
£500k Drumskin on Sgt. Pepper album cover
The lots were part of Sotheby's sale also featuring a grand piano used in almost all of Abba's studio recordings between 1973 and 1977, which did not sell.
Instruments, clothing and manuscripts from the collection of Cream bassist Jack Bruce sold for between £688 for a manuscript book to £9,750 for a Warwick Fretless Thumb Bass.
A powder blue Fender Stratocaster played by Eric Clapton sold for £45,000.
The original contract signed by The Beatles and manager Brian Epstein has sold at Sotheby's for £365,000.