Now, plans by an American company to salvage them and keep half the precious metals they carried have prompted accusations of modern-day piracy by critics in Jamaica who blame the government for selling off their national heritage.
Last month the Atlanta-based corporation Admiralty launched an expedition from Port Royal, a colonial-era pirate town once dubbed the "wickedest city on earth" to scour Pedro Bank, an area roughly the size of Jamaica itself, where the wrecks are believed to lie. It plans to search the seas for an estimated 300 ships which between them could yield a bounty worth billions of dollars.
Under a deal sealed in 1999 after intense lobbying, Admiralty persuaded the Jamaican government to reverse a previous ban on offshore treasure hunting and issue a licence to explore the area.
Ainsley Henriques resigned as president of Jamaica National Heritage Trust, the government agency overseeing the project, in protest at the deal. He told the Associated Press: "You're not just dealing with treasure here. All archaeology is really looking at is the frozen history of people. If you just suck it out for the gold you lose the story. And these stories are important, perhaps more important than the intrinsic value of the treasure itself."
Others also fear the government may be violating a 2001 United Nations convention banning the commercial salvaging of historic shipwrecks.
Representatives of Admiralty claim their aim is not to plunder but to resurrect, recover and preserve.
"I believe the critics are being critics for the sake of being critics," said Clarence Lott, Admiralty's vice-president. "We're not going to just go down there and tear everything up to get the gold. We're not a smash and grab operation. We recognise we have an archaeological responsibility. Jamaican government observers will be there throughout and have the right to stop anything they are not happy with. The truth is they don't have that culture right now because it's under water."
One of the sunken ships, the Genovesa, is a Spanish galleon which sank in 1730 with several tonnes of gold and silver on board and a cargo estimated to be worth around £330m.
Under the deal the Jamaican government and Admiralty will split equally the value of any precious stones and metals found, after covering Admiralty's expenses. All other valuable historical items, be it pottery, canons or other artefacts, will go to the Jamaican government.
"We know we're going to benefit," says Susanne Lyon, the executive director of Jamaica National Heritage Trust.
Admiralty plans to spend more than £1m in the first year of operation and says the excavation could take five years to complete. "We are bearing all the risk," says Mr Lott.
In an attempt to detect the precious metals without large-scale excavation and disturbance of the site, Admiralty will rely on new technology using electromagnetic waves. "It allows us to use a scalpel instead of a sledgehammer," said Ken Vrana, one of several archaeologists among Admiralty's crew.
But others are sceptical. When the agreement was first made five years ago, the head of Texas A&M University's nautical archaeology programme, Professor Donny Hamilton, told the Los Angeles Times: "Admiralty really does think there's hundreds of millions of dollars on the Pedro Bank. And I'm sure they believe in their technology. But to me, it's a bunch of hogwash."