He was great-grandson of Eärendil the Mariner (Eldarion is descended from Eärendil on both sides of his family and in him the two genealogical lines of the Half-elven are reunited), through his Half-elven mother Arwen; he was also the nephew of the Half-elf lords Elladan and Elrohir.
King Eldarion (his name meaning "from the Elves" in reference to his mother Arwen) was "full ripe for kingship" at the time, and ruled for an unspecified amount of time well into the Fourth Age of Men.