Much of what we know about its origins is a matter of guesswork. It was almost certainly the work of English embroiderers, and was most probably produced in the famous embroidery works of Winchester. The best guess is that it was commissioned by Odo, bishop of Bayeux, William the Conqueror's half-brother, and one of the leading figures in the invasion of England. It was perhaps completed on 1077 in time for the consecration of the new cathedral at Bayeux. Or perhaps it was finished in 1083.
Historians can argue endlessly about such things.
Some have suggested that it was hung around the nave of Bayeux cathedral on feast days, but it doesn't seem to have made for that specific purpose since it is not long enough to reach completely around the nave. During the French Revolution, it was hauled out to cover a wagon-load of ammunition being sent to the northern front where the Republican French were being attacked by Monarchist enemies. A young lawyer of Bayeux pulled the tapestry from the wagon and replaced it with a oiled and waterproof cloth much better suited for the purpose. He carried the tapestry home, and hid it in his attic, where it remained for the next thirty years. When it as brought out, it was turned over to the bishop of Bayeux, who placed it in the bishop's palace.