The first of the boys aged 11 to 16 made the treacherous two-and-a-half mile journey to safety on Sunday and the following day, four more were rescued.
The leader of the operation, acting governor Narongsak Osottanakorn, who had previously dubbed it “Mission Impossible”, said it had become “Mission Possible for Team Thailand”.
He added: “Nobody thought we could do it. It was a world first.”
Referring to the multi-national team that assisted in the rescue, he said: “The heroes are people from all over the world. This mission was successful because we had power. The power of love.”
The extraordinary 72-hour operation, led by expert British cave diver Richard Stanton, has involved rescue experts from 18 countries working with the Thai forces.
Mr Osottanakorn added that parents of the last batch of children would be allowed to visit their loved ones at the hospital last night.
The Thai Navy Seal unit orchestrating the mission confirmed on its Facebook page that the remaining children, said to be the weakest of the group, had been guided out of the tunnel network.
A statement read: “We are not sure if this is a miracle, a science, or what. All the 13 Wild Boars are now out of the cave. Hooyah.”
The 13, who became stranded on June 23 after heavy rains trapped them underground, are now recuperating in hospital in the nearest city, Chiang Rai.
To avoid the risk of infection, they are being kept in isolation and so are still separated from their parents by a glass window.
The group were discovered huddled on a sandbank within the six-mile cave system by Mr Stanton and fellow Briton John Volanthen, last Monday.
Officials said the boys rescued from the labyrinthine Tham Luang caves were in good health overall.
Two are believed to have pneumonia but the first eight boys to surface have recovered enough to ask for bread with chocolate spread for their breakfast instead of bland porridge.
The children originally set out to explore the cave and have a picnic to celebrate a birthday.
Jubilation over the rescue was tinged with sadness over the loss of a former Thai navy diver volunteer Saman Gunan, 38, who died on Friday when he ran out of air on his return journey from delivering oxygen tanks to the cave.
His wife Waleeporn Gunan paid tribute to him yesterday, saying: “Every day before we left for work, we said we loved each other. He has been praised as a hero. He was.”
She added: “I want to tell you, honey, you are the hero in my heart. You always were and always will be.”
The fate of the boys has been followed around the world.
US President Trump said their rescue was “a beautiful moment”. Prime Minister Theresa May said: “Delighted to see the successful rescue.
“The world was watching and will be saluting the bravery of all those involved.”
Hollywood producers are already plotting to turn the saga into a blockbuster film. Adam Scott, of Pure Flix films, said: “I see this as a major Hollywood film with A-list stars”.