The specimens, described as crocodile-like animals with fins instead of limbs that likely lived in shallow water, fill a gap in evolutionary knowledge of how sea creatures moved onto dry land and evolved into tetrapods, the four-footed animals that emerged from water.
The remains were unearthed from river sediments on Ellesmere Island in Canada's Nunavut, and the species has been dubbed Tiktaalik roseae.
The animal is described as looking superficially like a crocodile, with a skull of around 20 centimetres long, and a flattened body of between 1.25 and 2.75 metres, covered in diamond-shaped bony scales.
It is like a fish, with its primitive jaw and fins, but has a tetrapod's neck and ribs.
"It sort of blurs the distinction between fish and land-living animals," said one of its discoverers, palaeontologist Neil Shubin of the University of Chicago.
Experts said the discovery, with its unusually well-preserved and complete skeletons, reveals significant new information about how the water-to-land evolution took place.
"It's an important new contribution to (understanding) a very, very important transition in the history of life," said Robert Carroll of McGill University in Montreal.
What is generating the most excitement are joints in the fish's pectoral fins, which have bones that compare to the upper arm, forearm and primitive parts of the hand of land-living animals.
"Most of the major joints of the fin are functional in this fish," said Mr Shubin, whose findings will appear in the British science weekly Nature.
"The shoulder, elbow and even parts of the wrist are already there and working in ways similar to the earliest land-living animals," he said.
The sediment in which Tiktaalik was found has been dated to around 375 million years ago, in the swampy primeval era known as the Devonian.
At that time, what is now frigid Arctic Canada had a balmy, sub-tropical climate, for it was part of a mega-continent that straddled the equator.
Tiktaalik's size and shape indicates that it swam in small streams in a delta system -- an environment that probably encouraged the fish to venture into shallow water or even make forays onto land in search of food or shelter from predators, according to Mr Shubin.
"The skeleton of Tiktaalik indicates that it could support its body under the force of gravity, whether in very shallow water or on land," said co-author Farish Jenkins, a professor of organismic and evolutionary biology at Harvard University.
"This represents a critical early phase in the evolution of all limbed animals, including humans -- albeit a very ancient step."
Evolutionary biologists have hailed the find as ground-breaking, saying Tiktaalik fills a knowledge gap about a key transition period spanning around 20 million years in the Devonian era, between fish and the first tetropods.
The creature's name comes from the traditional Inuit language of the area, and refers to a large freshwater fish seen in the shallows.