They believe a Canadian lynx was prowling around the fields of the South West in 1903 before being shot after attacking two dogs in Devon.
Tests on the animal revealed it had probably spent some time in captivity before escaping or being set free.
The animal had been donated to Bristol Museum at the time of its death and kept in its stores for decades.
The scientists' findings are published in the journal Historical Biology.
Dr Ross Barnett, a molecular biologist from the University of Copenhagen and the University of Durham, said:  "I've seen one of these cats in the wild.
"They are pretty impressive cats - they are a reasonable size, and they have lots of fluffy fur which makes them look even bigger. They have sharp claws, teeth and strong muscles."
From blurry photos of the Beast of Bodmin Moor in Cornwall, to reports of a lion on the loose in Essex in 2012, the UK has a long tradition of spotting big cats.
Most of these claims are dismissed as misidentifications, hoaxes or even hallucinations, but not in this case.
In 1903, the unusual cat was donated to the Bristol Museum and Art Gallery. The museum's records state that it had been shot after attacking and killing two dogs close to Newton Abbot in Devon.
Unsure of exactly what it was, the exotic beast was stuffed, its skeleton preserved, and then the remains were tucked away in the museum's stores.
More than a century later, the cat was unearthed by a scientist who thought the find might be significant.
An analysis of the skeleton and mounted skin revealed that the animal was a Canadian lynx, which is about two to three times the size of a domestic cat and is usually found in Canada and the northern states of the US.
The researchers found that the animal's teeth were badly decayed.
Dr Barnett said:  "We think it had probably been in captivity at some point in its life.
"It had lost all of its incisors, which would have been a pretty debilitating injury for a wild cat, but not a problem for one in captivity.
"It also had massive amounts of plaque on its molars, which are indication of it not having a wild diet - something with lots of wet cat food, essentially ready-processed meat like steaks."
The researchers believe that the lynx had been in captivity for some time, but they were unable to find any records of the cat's owner.
"Was it someone's pet? Was it part of a small menagerie that was travelling through the area? There aren't really any zoos nearby where it could have escaped from," Dr Barnett said.
The team is also unsure how long the animal had been at large in Devon before it was killed.
Its decayed teeth would have limited its chances in the wild, but the lynx is an adaptable animal, and may have been able to survive by preying on small mammals.
While many big cat sightings remain unverified, sometimes the rumours do turn out to be true, and the team believes that the Canadian lynx is the earliest recorded example of an exotic cat on the loose in the UK.
Another case relates to a live puma that was captured in Inverness-shire in 1980 and had been living in the wild for a long period of time. It was called Felicity, and placed in a zoo.
But Dr Barnett said that these cases were few and far between.
He said: "It's all very good saying you saw a lion in Essex or a tiger in Shropshire, or wherever. But it is very difficult to estimate size of a species from a distance - especially if you are unfamiliar with them.
"So I would argue for continued scepticism, unless you have a body or specimen you can analyse."
A "big cat" was on the loose in the English countryside at the turn of the last century, scientists say.