Appropriately, it was the Thai Navy SEALs — heroes one and all, and none more so than former Seal Suman Gunan, who died during the rescue effort last Friday — who announced that the incredibly dangerous and difficult mission had been completed.

"12 Wild Boars [the name of the soccer team] and the coach out of the cave. Everyone safe," the unit wrote on its Facebook page.

"We are not sure if this is a miracle, science, or what. All the thirteen Wild Boars are now out of the cave," they later added.

Cheers went up as the rescue mission chief, Narongsak Osottanakorn, announced during a press conference hours later that the final people, three SEALs and a Thai doctor who had stayed with the boys overnight, had exited the cave.

"Mission accomplished," he said, adding that the global rescue effort was a "role model for the world".

The SEALs, joined by an "all-star" team of international divers, had begun the third day of operations at 10.08am local time [1.08pm AEST] needing to extract four more boys and the coach, as well as the three SEALs and Thai doctor who had stayed with the boys since they were miraculously first found by British divers eight days ago, and nine days after first going missing.

The rescue team exceeded expectations in every sense, overcoming obstacles including incredibly tight, dark conditions within the cave complex, huge volumes of water, health concerns about the boys and their total lack of experience diving.

Sunday's mission had saved four boys in 11 hours, while Monday's had achieved the same number in nine hours. On Tuesday, four boys and one coach came out in about nine hours and were followed soon by the remaining four rescuers who had stayed behind each night to care for the trapped boys.

Australian doctor Richard Harris, who is also an expert cave diver and whose presence was requested by British divers participating in the mission, played a critical role in the rescue operation on all three days.

Harris had swum all the way through the cave each day – about 3.2 kilometres – to the trapped Thai soccer players and given a medical sign off for each boy before an evacuation was attempted.

Each day, he would leave the cave only after the last boy had left.

Six Australian Federal Police divers and an Australian Navy diver also participated each day in key support roles.

Auttaporn Khamheng, 17, a close friend and former teammate of 13-year-old Duangpetch "Dom" Promthep and who is also close to the 25-year-old coach, Ekaphol "Ake" Chantawong, told Fairfax Media that he was ecstatic about the rescue of his friends.

"I am very, very happy to hear they have all come out and are safe, I am so happy," he said.

"I want them all healthy soon so I can play football with them again."

He had a specific message for the coach: "Don't blame yourself, because you are our world."

The parents of the boys have already said they don't blame coach Ake, who has nevertheless asked for forgiveness.

Seventeen days after the boys went missing and eight days after they were found, the round-the-clock mission had begun under dark skies and after 12 hours of heavy rains.

The four members of the “Wild Boars” soccer team and the coach had been left behind in the cave on Monday night after the second group of four boys was evacuated.

The already exhausted rescuers had to dig deep and plough on through soaring temperatures, rising humidity and thick mud on Tuesday.

As the minutes stretched into hours under the hot sun in this corner of north-western Thailand bordering Myanmar, hopes rose that good news was imminent.

When news of the successful operation broke, huge cheers went up from Thai volunteers at the media centre, a car park full of the world's press about 1.5 kilometres from the cave entrance.

The rescue effort has transfixed Thailand for more than two weeks and captured global attention for days on end.

In a briefing just before noon, local time, mission chief Narongsak Osottanakorn — who has become the international face of the rescue effort — said 19 divers (up from 18 on Sunday and Monday) would participate in the final push to bring the unprecedented operation to its conclusion.

Because of the heavy rains, which eventually eased in the afternoon, Narongsak said the decision had been taken to "not to waste time … for the third planned mission".

"We can do it [extract everyone] because we now have experience.

"From the first day to the second day we can do it two hours faster. The first day we spent 11 hours, yesterday we spent nine hours [from the start of the mission to the final rescue].

"Today [Tuesday] we might have to wait longer, but it will be worth the wait."

As a result of the rise in the number of people to be evacuated, Narongsak cautioned that Tuesday's mission would likely take longer. But "if everything goes right, we will see four kids and the doctor and the [three] SEALs that have stayed with the kids all come".

Hours later, he fronted the world's media to announce that the operation had bee a success. He hugged Third Army deputy chief Chalongchai and other military bosses, finally able to smile and let out a sigh of relief.

Earlier, Dr Jesada Chokedamrongsuk, the secretary of the Ministry of Public Health, provided a detailed briefing on the health of the eight boys who had already been rescued.

Two of the first boys had mild lung infections, which could be pneumonia but, he said, most of the boys were "fine, normal" and had undergone a battery of tests, X-rays, and received vaccinations.

After initially being fed further power gel energy rations, the boys had moved to eating soft, boiled rice and had even asked for and received chocolate.

The second group of four were, if anything, in slightly better condition, though one boy had a very low body temperature and a slow heart rate.

Both groups were brought out of the cave with gauze over their eyes because of their prolonged stint 3.2 kilometres deep inside the cave, Dr Chokedamrongsuk said, and had initially worn sunglasses at the hospital to soften their exposure to the light of the outside world.

The first group saw their parents and close family on Monday night, though through glass as they remained under quarantine, and the second group was scheduled to do so on Tuesday evening.

All of the boys are expected to remain in quarantine for up to a week before finally being allowed to go home and return to a life that will, likely, never quite be "normal" again.

The identities of the boys have not been confirmed by Thai authorities, but the first four boys brought out were aged 14 to 16 years old and the second group were 12 to 14 years old.