He was the son of Eurycleides, and was chosen as commander in 480 BC because the other Greek city-states did not want to serve under an Athenian, despite the Athenians' superior naval skill. He was, however, assisted by the Athenian Themistocles, who led most of the fighting.
His first act as commander was to sail the fleet to Euboea to meet the Persian fleet. When they arrived the Greeks found that the Persians were already there, and Eurybiades ordered a retreat, although the Euboeans begged him to stay. Instead, they bribed Themistocles to keep the fleet there, and Themistocles used some of his bribe to pay off Eurybiades (at least according to Herodotus, who is biased against Themistocles). The subsequent Battle of Artemisium was indecisive, and the Greeks removed their fleet to Salamis Island.
Eurybiades did not want to fight at Salamis either, but once again Themistocles convinced him to stay by threatening to withdraw the Athenian fleet (the largest contingent of the Greek forces). The Battle of Salamis was a decisive victory for the Greeks. After the battle Eurybiades was opposed to chasing the Persian fleet, and also to sailing towards the Hellespont to destroy the bridge of ships that the Persian king Xerxes I had built there. He wanted Xerxes to be able to escape rather than have him remain in Greece where he would possibly renew the land war.
Back in Sparta Eurybiades was rewarded with an olive wreath for his success at Salamis; Themistocles was given a similar reward.