We're never told exactly how old the Great Willow was, but the 'Old' in his name seems well earned, and he was clearly far, far older than any normal tree. He was in fact one of the most ancient of trees in the Old Forest, ' ...ageing no quicker than the hills, the fathers of the fathers of trees, remembering times when they were lords' (The Fellowship of the Ring I 7, In the House of Tom Bombadil). The wording here is vague, but it seems to date the willow back to the time even before the Elves came into the west, making him thousands upon thousands of years old.