Eitan reportedly fell from a breakwater structure into rough seas in the early morning on Tuesday and drowned at the port where he was working as an adviser to a construction company.
Helicopters and rescue ships launched a search and he was found after two hours, but medics were unable to resuscitate him, emergency officials said.
Eitan was born in northern Palestine in 1929, and in his late teenage years joined Jewish groups such as the Hagana and Stern.
He was wounded in action several times, including in the 1956 Sinai campaign - backed by Britain and France - against Egypt.
During the Israeli invasion of Beirut in 1982, he ordered the bombardment of the city, causing thousands of civilian casualties.
He served out his term in disgrace after the official Kahan State commission of inquiry faulted him for failing to prevent the massacre of hundreds of Palestinians by Israeli-allied militiamen at Lebanon's Sabra and Shatila refugee camps in 1982.
But the commission did not recommend any action against him.
In the mid-80s he founded two right-wing parties called Tehiya and Tsomet, which called for the expulsion of non-Jews from Palestine.
Eitan earned notoriety for his comments against Arabs and for opposing interim peace deals with the Palestinians in the mid-90s.
He served as agriculture minister and environment minister in Benjamin Netanyahu's government and was appointed to the post of deputy prime minister.
But his party failed to win support in a general election in 1999 and he left political life.