Arthur was born an illegitimate child of King Uther Pendragon and Lady Igraine. Uther became obsessed with Igraine, of whom was already married. It came to the point that Uther pleaded with his dearest friend and royal advisor, Merlin to allow him to quell his desires. Merlin agreed to use his magic, but at the price of a promise. That promise being that the child conceived of the union would be forfeited to Merlin for him to do with as he saw fit. Uther hesitantly accepted the offer and was disguised as Igraine’s husband. Arthur thus was conceived and handed to Merlin at the time of birth. Not being able to raise the child himself, he employed Sir Ector a lord of Camelot to raise him.
Growing up, Arthur knew nothing of his true parentage. Living under the assumption that Sir Ector was his father. Merlin over time became a mentor and trusted friend of the forgotten heir. Enlisting as a soldier at the mere age of 16, Arthur showed true promise in the Kings Army. When time came he answered the call to lift Excalibur from the stone.
The rest… hasn’t been written yet.