Eurotas was the son of King Myles of Laconia and grandson of Lelex, eponymous ancestor of the Leleges. The Bibliotheca gave a slight variant of the mythological generation of Eurotas, who was described as the son of Lelex, born from the ground, by his wife Cleocharia. In some accounts, his mother was called Taygete instead. Eurotas had no male heir, but he did have two daughters, Sparta and Tiasa, by Clete.

Eurotas bequeathed the kingdom to Lacedaemon, the son of Zeus and Taygete, after whom Mount Taygetus was named, according to Pausanias. This Lacedaemon married his daughter Sparta and renamed the state after his wife.

Pausanias says: "It was Eurotas who channelled away the marsh-water from the plains by cutting through to the sea, and when the land was drained he called the river which was left running there the Eurotas." The "cutting through" is seen by Pausanias' translator and commentator, Peter Levi, S.J., as an explanation of the Eurotas (or Vrodamas) Canyon, a ravine north of Skala where the river has cut through the foothills of Taygetus after changing direction to the west of the valley.

River gods are typically represented in Greek art, such as on coin motifs, as figures with the bodies of bulls and the faces of humans. If only the face appears, they might wear horns and have wavy hair, or be accompanied by fish. Claudius Aelianus states that the Eurotas and other rivers are like bulls.