Its origins can be traced way, way back to the Welsh works - although then it went by the name Caledfwlch. It can also be traced back to Irish mythology. Perhaps, Caledfwich was just a name given to swords in general - but for some reason, the name became associated with Arthurian legend and more importantly, it was the name given to Arthur's sword.
Monmouth is again, responsible for placing this sword in Arthur's hands. In The History of the King's of Britain, c.1136, Monmouth, Latinised the name of the sword and it became known as Caliburnus and he stated that it was forged in the Isles of Avalon...and his story kind of stuck.
Geoffrey Gaimer - an Anglo-Norman Chronicler who wrote the History Of The English People, carried on with this theme "...this Constantine was the nephew of Arthur, who had the sword Calibure..."
By the time Chrétien de Troyes got his hands on the story...
Merlin - series 4, episode 13