This was the fate of Arda, dating back to the original Music of the Ainur, as described in the Silmarillion:
And some have said that the vision ceased ere the fulfilment of the Dominion of Men and the fading of the Firstborn...
Aragorn's coronation in Lord of the Rings is precisely this moment - the Dominion of Men - and Gandalf even uses these exact words when describing it (in The Steward and the King, Book 6 Chapter 5):
This is your realm, and the heart of the greater realm that shall be. The Third Age of the world is ended, and the new age is begun; and it is your task to order its beginning and to preserve what may be preserved. For though much has been saved, much must now pass away; and the power of the Three Rings also is ended. And all the lands that you see, and those that lie round about them, shall be dwellings of Men. For the time comes of the Dominion of Men, and the Elder Kindred shall fade or depart.
The nature of the Elves is to fade, and Tolkien describes the reason for this in a passage entitled "Of Death and the Severance of Fea and Hroa" among the Finwe and Miriel materials, published in Morgoth's Ring:
As ages passed the dominance of their fear (i.e spirits) ever increased, 'consuming' their bodies. The end of this process is their 'fading'...
So, during the Lord of the Rings time period, we have the Elves starting to fade, and the Dominion of Men beginning, which were both foretold from the creation of the world, and also due to the nature of the Elves as-designed.