They will be taken to a nearby helipad with a police motorcycle escort before being flown to the provincial capital of Chiang Rai for treatment in a hospital there.
Several of the boys emerged from the cave on Sunday, about eight hours after 18 divers began their operation to free them.
Thirteen medical teams were stationed outside the cave - each with its own helicopter and ambulance - one for each of 12 boys and their coach.
"What we have today is the best situation", Narongsak told reporters from across the world who were gathered at the Pong Pha sub-district administration office opposite the Tham Luang Forest Park.
Two divers were to accompany each of the boys, all of whom have been learning to dive only since July 2, when the first searchers found them.
Mr Narongsak said that the rescue operation could take a number of days or be halted at any time.
Protester removed from Statue of Liberty after immigration demo
After almost four hours on the statue, the woman finally accompanied police down off the monument, tethered to them by wires. As they approached, she initially moved away, took off her shoes and appeared to be starting to climb further.
"It's about rain falling here, but it's also about rain falling in the area", he said.
The expedition started normally but things took a wrong turn when the group reportedly got stranded in the dark tunnels by a sudden inflow of water into the caves from the heavy rain. The Thai official in Sunday night's news conference said rescue workers need "about 10 hours" to prepare for next operation.
The boys, aged between 11 and 16, went missing with their 25-year-old coach after soccer practice on June 23, setting out on an adventure to explore the cave complex near the border with Myanmar and celebrate a boy's birthday, reported news agency Reuters. Monsoon flooding cut off their escape and prevented rescuers from finding them for nearly 10 days, CBS News reported.
An undated image of Thai military personnel inside a cave complex during the ongoing rescue operations for the youth soccer team and their assistant coach.
USA president Donald Trump confirmed this morning in a tweet that the United States is among the six countries assisting Thai officials. Very courageous and talented people!,' the president wrote on Twitter Sunday morning.
To ensure a clear path for getting evacuees to the hospital and to safeguard their privacy, authorities ordered the media to move away from the cave before the boys came out.