"This is the most valuable treasure that has been found in the history of humanity," President Juan Manuel Santos declared on Saturday.
He was speaking from the northern port city of Cartagena, close to where experts made the hugely valuable find.
Treasure hunters had searched for the ship for decades, described by some as the holy grail of shipwrecks.
The loot is estimated to be worth around $2 billion, its value having dropped significantly due to the falling price of silver, according to US-based company Sea Search Armada.
SSA, whose subsidiary claimed in the early 1980s that it had found the galleon's final resting place, was engaged in a long-running battle with the government of Colombia.
The find was not confirmed and a US court ultimately ruled it was Colombian property.
The San Jose has long been the source of fascination and popular legends, and even figures in Gabriel Garcia Marquez's "Love in the Time of Cholera."
Mystery solved after centuries
Although they found plenty of other wrecks, the San Jose's location had remained a mystery until now.
The San Jose was sunk in June 1708 near the Islas del Rosario, off Colombia's Caribbean coast, during combat with British ships attempting to take its cargo, as part of the War of Spanish Succession.
The galleon was the main ship in a treasure fleet carrying gold, silver and other valuable items from Spain's American colonies to King Philip V.
Only a handful of the ship's crew of 600 survived when the San Jose sank.
A team of Colombian and foreign researchers, including a veteran of the group that discovered the wreck of the Titanic in 1985, studied winds and currents of the Caribbean 307 years ago and delved into colonial archives in Spain and Colombia searching for clues.
Experts confirmed that they found the San Jose on November 27 "in a place never before referenced by previous research," Santos said.
At least five other major shipwrecks were discovered when searching the ocean floor.
The experts confirmed that they located the San Jose, which was lying on its side, identifying it by its unique bronze cannons with engraved dolphins.
"The amount and type of the material leave no doubt of the identity" of the shipwreck, said Ernesto Montenegro, head of the Colombian Institute of Anthropology and History.
There could be up to 1,000 shipwrecks off the Caribbean coast of Colombia, but of those only between six and 10 had a large cargo of treasures, anthropologist Fabian Sanabria told AFP.
The biggest find, and the most sought after, was the San Jose, he said.
The discovery "is an unprecedented event for the country," said Cartagena Mayor Dionisio Velez.
On Twitter, the issue was trending under #GaleonSanJose, as users of the one-to-many social network debated whether to return the loot to Spain, and made various estimates about its current value.