The grave, found by Peter Anderson, who was carrying out renovations on his house in April, is now being investigated by Historic Scotland.
“I was digging out the floor to put insulation ducts in for a ground source heat pump, and came across the bones.
“I actually didn’t see much of what was there because we didn’t disturb it.
“There was a leg bone and possible rib bones, and at that point we stopped.”
County archaeologist Julie Gibson was contacted, and AOC Archaeology Group, which is contracted by Historic Scotland to deal with human remains, subsequently came out to Papay to exhume the body.
Mr Anderson, who is originally from West Yorkshire, said: “What I have been told is it’s a boat burial, one of ten in the whole of Scotland.”
Mr Anderson bought the property in 2011, but only moved in last April. However, in February, before he took up residence, potential viking remains were found 150 metres to the south of the latest discovery.
Since the recent find, archaeologists have been busy taking photographs and mapping the property and are due to return soon to complete their excavations, although a date has yet to be confirmed.
As well as the human remains, Mr Anderson said the archaeologists had also made a number of other significant discoveries, such as a shield boss.
“They also found lots of nails and, when these were plotted on the computer, they were in the shape of a boat,” he said.
“Also, in the sand you can see the staining of the timber, although the wood has long since rotted away.”
A spokesperson for Historic Scotland said: “We were recently made aware of what appeared to be human remains being found during building work on Papa Westray.
“Under the terms of the Human Remains Call Off contract, AOC Archaeology visited the site, with initial analysis suggesting they were from a Norse burial site.
“Further analysis of the findings has taken place off site, and a team from AOC will be returning to the site later this month to complete the investigation.”