A helicopter flew the four boys to the nearby city of Chiang Rai, where they were taken by ambulance to hospital.
The next operation will begin in 10 to 20 hours and will involve 90 divers, he said.
It's unclear how long the complex and risky rescue effort will take, but it could be days.
"Today, everything was very smooth", Narongsak said.
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Wild Boar Academy have spent more than two weeks in the Tham Luang caves after being cut off from the exit during a visit by a sudden downpour.
Narongsak Osottanakorn, who is in charge of the rescue mission, said Saturday conditions were now "perfect", BBC News reports.
Water from heavy rains have flooded the cave, leaving the team trapped inside.
Divers are guiding the boys in darkness through tight and hard passageways.
Speaking to reporters at a briefing near the cave on Sunday night, Chiang Rai provincial acting Gov. Narongsak Osatanakorn said the healthiest boys were taken out first, with the first two emerging at 5:40 p.m. and 5:50 p.m. local time, or 6:40 a.m. ET.
"Four boys have reached chamber three and will walk out of the cave shortly", Lt. On Saturday, a doctor examined the boys and said they were in good health.
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Eight members of the soccer team, ages 11 to 16, and their 25-year-old coach remain trapped in the cave.
Narongsak, who is heading the operation, said earlier Sunday that 13 foreign and five Thai divers were taking part in the rescue, and two divers were to accompany each of the boys, all of whom have been learning to dive only since Monday, when the first searchers found them. The most problematic section of the trip has been revealed to be halfway out and named the "T-Junction" sue to the fact that it is so small divers are forced to remove their air tanks to pass it.
Within minutes the boys emerged from the Tham Luang cave complex and were immediately placed into ambulances and rushed to a hospital, authorities told ABC News.
They spent nine days unaccounted for inside the cave, before British divers found the emaciated and dishevelled group huddling on a muddy bank. Other divers were on guard along the risky first kilometer of the passageway.
Heavy rains are expected to continue in the coming days while breathable air inside the cave dropped to concerning levels, hastening the need for their escape.
Cave rescue experts have said they consider an underwater escape to be a last resort, especially with people untrained in diving.
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"It is important to appreciate that the United Kingdom cave divers continue to work alongside the Thai Navy SEAL divers and a combination of cave divers and open water divers from many other nations", the statement said.