Pinera said the nation was "crying with excitement and joy'' after engineers broke through on Sunday to the men's refuge.
It had been 18 days since a landslide at the gold and copper mine caused a tunnel to collapse and entombed them more than 2,200 feet below ground.
Doctors and psychological experts meanwhile were trying to safeguard the sanity of the miners in the months to come, and said they were implementing a plan that included keeping them informed and busy.
"They need to understand what we know up here at the surface, that it will take many weeks for them to reach the light,'' health minister Jaime Manalich told the Associated Press.
President Pinera has sacked top officials of Chile's mining regulator and vowed a major overhaul of the agency in light of the accident.
The Chilean President said the entire nation was elated to receive the good news. [AFP]
"Obviously, there is a degree of happiness," a beaming Mining Minister Laurence Golborne told state television from the mine entrance, where relatives of the trapped men have been camped out for over a fortnight.
"I thank the miners for their bravery, for their courage in holding out more than two weeks in the depths of the mountain," Pinera said.
"They'll come out thin and dirty, but whole and strong, because the miners have shown they have courage and mettle, which is what has kept them together."
Serious mining accidents are rare in Chile, but the government says the San Jose mine, owned by local private company Compania Minera San Esteban Primera, has suffered a series of mishaps and up to 16 miners have lost their lives in recent years.