Sebastian Pinera, the Chilean president, stunned the country on Sunday, when he announced that a written note sent through a bore hole proved that all the 33 miners were alive.
“All 33 of us are well inside the shelter,” said the note, written in bold red capital letters.
Rescuers discovered the trapped men when they heard hammering noises.
The men were working at the San Jose gold and copper mine near the city of Copiapo, 500 miles north of Santiago, at a depth of around 2,300 ft when the rock above them collapsed on Aug 5.
But amid the joy of the news of their survival, Andres Sougarret, the engineer in charge of the mission, said it could take months to free the men from their underground prison.
It would take “at least 120 days” to carve a second shaft that was wide enough for the miners to be pulled up one-by-one.
A camera lowered down the bore hole on Sunday showed the miners sweaty and shirtless in the hot (32-36 degrees Celsius, 90-97 Fahrenheit) shelter, but in apparently good condition and high spirits.
“Many of them approached the camera and put their faces right up against it, like children, and we could see happiness and hope in their eyes,” Chile’s president said, adding that the images had given him “a lot of happiness and faith that this is going to end well”.
Carlos Garcia, regional director of the National Emergency Office, said the trapped miners had water and lights and that in the next few hours they would be given fresh supplies of food and water, which they would have to ration carefully.
As word spread that the miners were alive after 17 days below ground, drivers honked their horns in the capital Santiago and thousands of people gathered in other cities to celebrate and wave national flags.
“Today all of Chile is crying with excitement and joy,” Mr Pinera said amid celebrations at the mine.
Until Sunday, there had been no sign that the miners had survived their ordeal.
The men have been trapped for one of the longest stretches in recent mining history. Last year, three workers survived 25 days trapped in a flooded mine in southern China, and two miners in north-eastern China were rescued after 23 days in 1983.
Few other rescues have taken more than two weeks.
The Chilean miners’ survival after 17 days is very unusual, but as they have survived so far, they should emerge physically fine, said Davitt McAteer, who was assistant secretary for mine safety and health at the US labour department under President Bill Clinton.
