Black had a UK Top 10 hit with the Lennon/McCartney-penned It's for You in 1964, which was produced by George Martin at Abbey Road Studios.
The song peaked at number 7 in the charts but Paul McCartney had earlier that year recorded his own version, clocking in at just under two minutes, on a seven-inch Dick James demo disc, for Black to listen to.
The acetate was delivered to the London Palladium, where Black was performing at the time, but its whereabouts since then had been unclear, and it was thought to have been lost or destroyed.
The disc has now re-emerged after a relative of Black, who died last year, came across a brown envelope which had the words 'It's For You' handwritten on the front and Cilla Black's name underneath.
They assumed that it was a copy of her hit record and brought it in with other items to be valued at The Beatles Shop in Mathew Street, Liverpool.
Stephen Bailey, manager of the shop for 31 years, said they decided to play what they thought were 21 demo discs by Black.
"We got to the last one and as soon as I heard it I thought 'oh God, that's not Cilla Black - it's Paul McCartney'," he said.
"I was shaking with excitement and speechless. I realised that this was the long-lost Beatles demo disc from 1964. I was probably one of the few to have seen and heard it in over 50 years.
"Apart from a few crackles, which you get with acetates, the quality is fine. It's a wonderful recording. I can't think of finding anything better, unless I discover there is a sixth Beatle.
"I urge all Beatles fans to search their bottom drawers and attics where they could have put Beatles memorabilia years ago and forgotten all about them. You just never know what it is worth."
The disc will go on sale on Saturday August 27 at the Beatles Memorabilia Auction in Liverpool, and is expected to fetch between €18,000 and €24,000.