It is unclear, even to Gandalf (at least as of The Hobbit, before the wizard and Beorn became friends) whether Beorn is fundamentally a man who can change into a bear, or a bear that can shapeshift into a man. As Gandalf puts it in "Queer Lodgings":
Some say that he is a bear
descended from the great and ancient bears of
the mountains that lived there before the giants
came. Others say that he is a man descended
from the first men who lived before Smaug or
the other dragons came into this part of the
world, and before the goblins came into the hills
out of the North. I cannot say, though I fancy the
last is the true tale. He is not the sort of person
to ask questions of.
At any rate he is under no enchantment but
his own. He lives in an oak-wood and has a
great wooden house; and as a man he keeps
cattle and horses which are nearly as
marvellous as himself. They work for him and
talk to him. He does not eat them; neither does
he hunt or eat wild animals. He keeps hives and
hives of great fierce bees, and lives most on
cream and honey. As a bear he ranges far and
wide. I once saw him sitting all alone on the top
of the Carrock at night watching the moon
sinking towards the Misty Mountains, and I
heard him growl in the tongue of bears: ‘The
day will come when they will perish and I shall
go back!’ That is why I believe he once came
from the mountains himself.
Although "came from the mountains" is ambiguous, to me this makes it sound as if Beorn himself may have been driven down out of the Misty Mountains when they became inhospitable—not merely that he is descended from men or bears who previously lived up among the heights. The Misty Mountains had been infested with orcs since at least the 2790s, when the War of the Dwarves and Orcs took place. Since Thorin and Company meet Beorn in T. A. 2961, Beorn seems to have been well over 150 at the time of The Hobbit. That is not beyond the limit of human lifespans in Middle Earth, but it does suggest that (beyond his ability to change shapes), Beorn is not a normal human.
On the other hand, we know from The Fellowship of the Ring, "Many Meetings":
Frodo learned that Grimbeorn the Old, son of Beorn, was now the lord of many sturdy men, and to their land between the Mountains and Mirkwood neither orc nor wolf dared to go.
From this it seems likely that Beorn was deceased by the year 3018, when Frodo arrived in Rivendell. Moreover, the fact that his son was given the cognomen "the Old" suggests again that Beorn's descendants also enjoyed longer lifespans than ordinary men.
The fact that Beorn seems probably to have died is also significant in another way. In general, the idea of intelligent, speaking animals (be they bears, wargs, ravens, or other) is actually somewhat difficult to reconcile with Tolkien's cosmogony, in which only those races given the Secret Fire by Eru possess free will and souls. Talking animals—both good and evil—crop up repeatedly in The Hobbit though, so there does need to be some place for them. It is sometimes suggested that, like the eagles (the emissaries of Manwë) all the other animals who talk—from Huan the Hound to the thrush who tells Bard of Smaug's weak spot—are actually Ainur in animal shapes. However, this seems not to be a viable explanation for Beorn, if did eventually die of old age.