A statement from Odyssey said the coins were legally imported to the US but did not give any details of their origin and the wreck was only referred to by its codename of "Black Swan".
The haul is believed to be the largest ever of its kind.
The silver coins alone weigh 17 tonnes and an expert consulted by the company recommended offering the silver coins at retail prices ranging from a few hundred dollars to $4,000 each, depending on the condition, date and origin.
"The gold coins are estimated to bring substantially higher numbers," the company said.
Odyssey said it had used a tethered underwater robot, also known as remotely operated vehicle, in the salvage operation.
"For site security and legal reasons, we are not prepared to give the location, depth or any other information about the site," the company said, adding that it planned further excavations once it has confirmed the name and nationality of the sunken ship.
"We have some interesting evidence that tends to point to a specific shipwreck, but we do not intend to discuss this publicly until we have had a chance to review contemporary records and conduct extensive analysis of the artifacts and coins that have been recovered to date," Odyssey said.
The company made it clear it wanted to assert its legal rights to the find before it would provide details of its location, but insisted the shipwreck was well beyond any country's territorial waters.
Earlier this week, a US court granted Odyssey ownership of the contents of a sunken ship located 100m below the surface and 64km off Land's End, near the English Channel. The wreck is believed to be of a 17th century merchant ship.
The company said it was discussing film, television and book rights.
It said the coins were shipped to the US, where they are being individually restored.