Experts have used ground-penetrating radar to make the find at the World Heritage Site near Ripon.
The abbey, which is one of the largest monastic ruins in the country, existed from the early 12th century until its closure in 1539 during the Dissolution of the Monasteries.
The National Trust, which looks after the site, has been working for more than two years on the project with experts from Bradford University, Geoscan Research and Mala Geoscience.
Their work has identified not only the location of the cemetery but also the formation of the graves which suggest that the monastic community believed in literal or corporeal resurrection.
The findings, backed up by documentary sources, show a ‘bunk-bed’ formation with the bodies clearly separated by stone partitions within the same grave.
This, together with regular organisation of the graves sited well away from each other, indicates the importance given to keeping the remains separate from later burials.
It supports the theory the community believed in literal or corporeal resurrection whereby a person’s physical remains would rise from the grave on the Day of Judgement. If the body was damaged, the soul would be as well.
This was unusual in medieval Christian communities, which focused on the welfare of the departed’s soul rather than their mortal remains.
Analysis of the images shows multiple burials in each grave cut, up to four in some cases, suggesting there could be up to 2,000 bodies in total. This number would account for the majority of the monks and lay brethren that died at the site.
National Trust archaeologist Mark Newman said: “This work has brought a startling and moving reconnection with the monks who once lived and prayed at this extraordinary site.
“The existence of a monks’ cemetery on the site has been known for centuries.
“Our conclusions about the formation of the graves are supported by reports from Victorian workmen at the site who uncovered some of the graves in several tiers which had already suggested multiple burials in the same grave cut.
“However, until now we did not know the exact location or scale of the cemetery.
“These findings are a profound and unexpected reminder that the monks have never really left Fountains Abbey. They’ve been here, at rest, some of them for almost 800 years.”
The images show the graves laid out in regular, curving rows running east from the abbey church, measuring approximately 80 metres by 60 metres.
Dr Chris Gaffney, from Bradford University, added: “The results at Fountains are little short of remarkable.
“Archaeologically they are among the most complete graveyards uncovered using geophysical techniques.
“As a general rule, burials are difficult to detect by geophysical means, so revealing the whole layout of a cemetery, in the way that we have, is exceptionally unusual.”