Among them were the last three Thai Navy Seals and Australian doctor Richard Harris, who had spent much of the past week keeping vigil with the trapped boys, the Guardian said.
The second group of boys rescued has been given approval to see their parents through glass, but the third group are still undergoing tests, he said.
The rescue mission which spanned days was a success after everyone was rescued.
Speaking earlier Wednesday, health ministry inspector Tongchai Lertvirairatanapong said the boys were in "good condition", despite each losing an average of two kilograms (4.4 pounds) in weight during their time in the cave.
Video has been released showing them in good health and in good spirits, though they will stay in quarantine for a week.
An American involved in the operation described the perilous zero-visibility dives that brought the boys out safely as a "once in a lifetime rescue".
Police officers took photographs of each other at the massive cave entrance, as pumps continued to suck out huge volumes of water.
The authorities had previously denied the children were drugged but Prayut Chan-o-Cha confirmed that they had been given an anxiolytic "to make them not excited, not stressed".
Elsewhere, Duangduen Sittiwongsa, a classmate of 16-year-old Pheeraphat "Night" Sompiengjai, whose birthday fell on the same day the team entered the cave, said they would give him cake and gifts when he returned to school. "Without him, in this operation, I don't think we could have succeeded".
Outside experts have said the group identity of the soccer teammates and their youth would aid their ability to recover.
Wrapped in foil blankets to keep them warm, the boys are threaded through a claustrophobic tunnel compared to the "S-bend" of a toilet.
The 12 boys and their coach were trapped after heavy rain in northern Thailand on June 23 but their rescue has now been completed.
The Wild Boars soccer team and their coach are expected to spend a week in hospital.
Some of the rescued boys in hospital. Lit by several beams of white light, the divers in wet suits and helmets are seen submerging themselves in the water and grabbing on to a metal dive line used to guide them through the winding channels of the six-mile cave. The stranded were in safe and experienced hands, however; two specialist divers accompanied each of them through their hard journey to freedom. "You can't blame the coach and you can't blame the kids", Thongchai said.
Kanthawong said he just wanted to support the team now that the players were out.
First, filmmakers need to secure the rights from each of the boys' families, the coach, and any rescuers they want to portray in order to get their firsthand accounts of what happened.