"The 12 Wild Boars and coach have emerged from the cave and they are safe," the Thai navy SEAL unit said on its official Facebook page.
The "Wild Boars" soccer team and their coach got trapped on June 23 while exploring the cave complex in the northern province of Chiang Rai after soccer practice and a rainy season downpour flooded the tunnels.
British divers found the 13, hungry and huddled in darkness on a muddy bank in a partly flooded chamber several kilometres inside the complex, on Monday last week.
After pondering for days how to get the 13 out, a rescue operation was launched on Sunday when four of the boys were brought out, tethered to rescue divers.
Another four were rescued on Monday and the last four boys and the coach were brought out on Tuesday.
Celebrations will be tinged with sadness over the loss of a former Thai navy diver who died last Friday while on a re-supply mission inside the cave in support of the rescue.
The head of the operation, Narongsak Osottanakorn, said earlier the final operation would be "more challenging" because one more survivor would be brought out, along with three Navy SEALs who have been accompanying them.
The rescuers have been learning from experience and were two hours faster in bringing the second batch of survivors out on Monday.
However, scattered monsoon rains continued to risk percolating through the limestone cave walls to flood the tunnels with fast-flowing water.
"I hope today we will be faster or the same speed as yesterday," Narongsak said.
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"All four boys have arrived at hospital, all are safe," Narongsak Osottanakorn, head of the rescue mission, told reporters of those freed on Monday.
Asked whether the remaining four "Wild Boars" team and their coach would come out at the same time in the next rescue effort, he said: "It depends on the plan... We have set the plan for four people so if they want to take five out (at the same time), then they need to change the plan."
The operation on Monday went more smoothly than on Sunday and took two hours less as the practice became more refined, he said.
Prime Minister Prayuth Chan-ocha visited the cave to inspect the operation, with navy rescuers giving him a rousing cheer.
"The prime minister said that this kind of event should never happen again on Thai soil," Narongsak said. "We should learn from this experience to prevent it from happening again."
SAVED BOYS ASK FOR CHOCOLATE BREAD
Meanwhile, the first eight boys rescued from a Thai cave complex are in good health overall and some asked for chocolate bread for breakfast, officials said on Tuesday as rescuers began a third and more challenging final mission to free the remaining five.
"At this moment (there are) no worrisome conditions, everyone is safe," Jesada Chokdamrongsuk, Thailand's health ministry permanent secretary, told reporters.
Two of the boys had suspected lung infections but the four boys from the first group rescued were all walking around their hospital beds.
"The kids are footballers, are strong and have high immunity," Jesada said when asked why they survived so long.
The boys had a good appetite but were mainly being given bland, easily digestible foods. However, doctors later relented after some of the boys asked for bread with chocolate topping.
They are still being quarantined from their parents because of the risk of infection and would likely be kept in hospital for a week to undergo tests, officials said.
Four more of the boys were carried on stretchers out of the labyrinthine Tham Luang cave on the Myanmar border on Monday, bringing to eight the total number brought out so far after two rescue pushes in successive days.
'RESCUE HAS BEEN IMMENSE'
The plight of the boys and their coach has drawn international attention, with divers, engineers and medics among others flying in from around the world to assist.
The team became trapped on June 23 when they set out to explore the cave after football practice and rains flooded the tunnels, trapping them inside. British divers found the 13 a week ago.
But the efforts to rescue the boys - aged between 11 and 16 - have proved a monumental challenge. Some were not even strong swimmers, and have had to learn to dive in conditions that claimed the life of a former Thai Navy SEAL on Friday.
Thirteen foreign divers and five members of Thailand's elite navy SEAL unit make up the main team guiding the boys to safety.
Authorities have said the boys are being held close to divers and wear oxygen masks to enable normal breathing.
"The rescue has been immense," said volunteer helper Somjit Saenset (56). "I'm so happy the children came out safely. I want to send my moral support for all involved" in the rest of the mission.
Narongsak said the rescued boys had not been identified out of respect for the families whose sons were still trapped, adding that the boys were being kept away from their parents due to fear of infection.
Medical teams previously said concerns included hypothermia and an airborne lung infection known as "cave disease", which is caused by bat and bird droppings.
Somboon Sompiangjai (38), the father of one of the trapped boys, said parents were told by rescuers ahead of Sunday's operation the "strongest children" would be brought out first.
"We have not been told which child has been brought out ... We can't visit our boys in hospital because they need to be monitored for 48 hours," Somboon told Reuters. "I'm hoping for good news."
The president of football's governing body, FIFA, has invited the boys to the World Cup final in Moscow on Sunday if they make it out in time.
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