The sources for Eluréd's date of birth (all of which appear in volume XI of The History of Middle-earth) are in some disagreement with one another. According to The Tale of Years in that source, Eluréd and his brother Elurín (there called Elrún and Eldún) were twins born in I 500. This was later amended, so that the brothers were born three years apart in I 492 and I 495, dates that also appear on a genealogical chart of the House of Bëor in the same volume.

I 506 is the date that Eluréd and his brother Elurín were last seen, but there is a small chance that they may have survived. In the sacking of Menegroth by the Sons of Fëanor, Celegorm's servants left the brothers to starve in the forests of Doriath. Celegorm's less cruel brother Maedhros tried to search for the lost children, but failed to discover them. The Silmarillion closes their story with the words '...of the fate of Eluréd and Elurín no tale tells.' This intriguingly ambiguous wording might be taken as a hint that they somehow survived their ordeal, but the brothers are never mentioned again after their loss in I 506.

Eluréd's mother Nimloth was a full Elf, but his father Dior was the son of Lúthien, an Elf, and Beren, a Man of the House of Bëor.

Eluréd's father Dior was the grandson of Elu Thingol, Lord of Beleriand, and thus Dior gained the title Eluchíl meaning 'heir of Elu'. Eluréd's name follows in this same tradition, and also means 'heir of Elu', though in place of the Elvish element -chíl (literally 'follower'), the name Eluréd contains rêda, the word for 'heir' in the Mannish Bëorian tongue of his grandfather Beren.