The One Ring is destroyed and the Tower of Barad-dur falls in the year 3761 BCE, bringing an end to the Third Age of Middle-earth. Both might have been different retellings of the same event. Tolkien never indicated when the World changed again so that the geography of Middle-earth was altered to the geography of the modern world however, it would have had to have been some event analogous to the Biblical Great Flood (2349 BCE). That would make the beginning of the Fourth Age at 3759 BCE.
We can tentatively assign that year to the Fall of Barad-dur and the end of the War of the Ring. That corresponds fairly well with the Modern Hebrew Calendar which places the beginning of the world at 3761 BCE. Tolkien wrote that the end of the Third Age would have happened about 6000 years ago.
