The variety of apple - believed to date back to the 13th Century when it was grown by monks - was spotted on remote Bardsey Island.
Visitor Ian Sturrock picked a fruit from an apple tree on a trip to the island off the north Wales coast and sent it to experts.
Experts at the Brogdale Agricultural Trust, in Faversham, Kent, have examined the apple and named it, appropriately enough, the Bardsey Apple.
Dr Joan Morgan - one of the world's leading experts on apples - said it was the only one of its variety in the world.
Unique variety
She said: "The apples were boldly striped in pink over cream, ribbed and crowned. We could not put a name to it - and who would wish it to be anything other than the Bardsey Apple?"
Brogdale is the home of the national fruit collection with more than 2,000 different varieties from all over the world.
The Bardsey apple has now been added to the collection.
Mr Sturrock plans to take cuttings from the single tree and grow the apples at his home on the mainland in Bangor, Gwynedd.
He said: "I took the apples off the tree to use in a bird trap.
'Rarest tree'
"I didn't realise the significance of the find until I took it to Brogdale. Dr Joan Morgan said it is the rarest apple tree in the world."
It is thought monks who lived on the island from the 13th Century might have cultivated the tree for food.
The apple also appears to be completely disease-resistant, which is unique for fruit trees in north Wales.
"If the monks were selecting trees over hundreds of years, they would have selected disease-resistant trees," said Mr Sturrock.