We are lacking almost any information about the origins of the Song of the Sun and Moon, but given its subject matter it must inevitably have been written after the making of the Sun and Moon. At its earliest, then, the song was made at the beginning of the Years of the Sun (that is, the last few centuries of the First Age, following the loss of the Two Trees).

As with its dating, the authorship of the Song of the Sun and Moon is also shrouded in uncertainty, but we do have some clues to work from. Given the level of detail within the song, we can take it that its maker either saw those events directly, or at least had access to an eye-witness. The song is also mentioned in the Annals of Aman (in volume X of The History of Middle-earth), and those Annals were said to have been the work of Rúmil of Tirion. None of this is conclusive, but taken together these various hints imply that the Song of the Sun and Moon was created in Aman, shortly after the events it describes.

None of this helps to explain how the song came to be mentioned in The Silmarillion, which contains material specific to the Noldor who returned to Middle-earth (which is problematic, because those Noldor departed before the Moon and Sun - and therefore the song - were made). The song must have somehow been carried across the Great Sea later in history (perhaps by one of the Wizards, for example) and eventually incorporated into the full Silmarillion account.