The unsafe underwater rescues - considered a last resort - involve two divers accompanying each of the boys, none of whom had experience diving before they were found on July 2.
This final mission aims to rescue the last remaining 4 members of the team, as well as their coach.
Celebrations will be tinged with sadness over the death of a former Thai navy diver who died on Friday while on a re-supply mission inside the cave.
Some 19 divers have re-entered Tham Luang Cave in northern Thailand and as with the previous rescues, two divers will escort each of the footballers out of the cave with tethers.
Officials were not immediately available to comment on who had been brought out, and their condition was unclear.
The remaining five members of the Thai soccer team will be rescued from the cave today, officials have confirmed.
Nineteen divers entered Tham Luang cave at 10.08am on Tuesday, hoping to bring out the remaining four boys and their football coach still trapped inside.
Those rescued Sunday traveled more than half a mile underwater, according to Chiang Rai Gov. Narongsak Osottanakorn, who is the head of the rescue mission.
After divers brought out four of the boys Monday evening, authorities indicated the rescue operation would continue for a third day.
A spokesperson from the Thai public health authority said that they were in "high spirits" and also claimed that as they are football players, they have high immune systems.
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The rescuers have been learning from experience and were two hours faster in bringing the second batch of survivors out on Monday.
The chances of monsoon rains raising water in the cave again, endangering their dry refuge and making the escape route too risky, were never far from the minds of everyone involved.
Narongsak decided on Sunday to launch the rescue operation after being assured the water had receded and the boys' health was improving thanks to nourishment given them by the SEALs team.
CNN was told the boys were exploring the caves on June 23 with their coach when they were trapped inside by heavy seasonal rains.
British divers found the 13 a week ago.
"We had imagined all sorts of catastrophic situations - equipment breaking, children panicking", he said, adding that the officials had backup options in mind in case anything falls apart.
He added that the boys were being kept away from their parents due to fear of infection they might have contracted in the cave.
Eight boys have so far been rescued from the cave, four on Sunday and another four on Monday.
All ten of the boys trapped in a flooded Thai cave have been rescued. "Mini-sub is ready if needed".
On Twitter, Musk has mused about potential inventions that could help the trapped soccer team, including a miniature submarine made from part of a SpaceX rocket.