British divers found the 13, hungry and huddled in darkness on a muddy bank in a partly flooded chamber several kilometres inside the Tham Luang cave complex, on Monday last week.
Chiang Rai Gov. Narongsak Osatanakorn had said earlier Tuesday that the day's effort might take longer than the previous two rescue missions, but the final four players and coach were out of the cave within 10 hours of the operation's start.
Samarn Poonan, 38, a former member of Thailand's elite navy SEAL unit, died last Thursday night as he worked underwater in the cave complex, laying oxygen tanks along a potential exit route.
The rescue missions take almost half a day to complete.
The first eight boys rescued from a Thai cave are in good mental and physical health and are asking for chocolate, officials said Tuesday, although two were on antibiotics after being tested for pneumonia.
Medical staff say the eight boys freed from the cave on Sunday and Monday are "healthy and smiling", but two may have a lung infection.
So far the group have been "kept away" from physical contact with their parents until the risk of infection is over and doctors have only allowed family and loved ones to see them through glass.
The rescued boys are being quarantined in case any of them contracted infections while inside the cave.
The second group freed on Monday were aged 12 to 14.
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Friends and family have identified the other three daughters as 17-year-old Danna and 13-year-old twins Allison and Melissa. It follows her husband and their four daughters being involved in a traffic accident which left all family members dead.
Today, the four remaining boys were confirmed to have been rescued and were taken to hospital after Reuters reported that those in charge of the rescue mission were "hopeful" all 12 boys plus the coach would be out today.
At least nine ambulances and a convoy of other vehicles were at the cave site Tuesday.
The plan, he said, is to bring out the four boys and their coach on Tuesday if the weather cooperates.
"The kids are footballers so they have high immune systems", Mr Jedsada said.
Operations to pump water out of the cave went on despite heavy rain showers on Sunday and Monday. Before the final rescue, he told CNN that divers inside the cave faced a number of challenges.
Musk said on Twitter: "Just returned from Cave 3".
"We would be honoured to welcome the team from the Wild Boars Football Club and their rescuers to Old Trafford this coming season".
"We were obviously very afraid of any kind of panic from the divers", he said, adding he was in awe of the boys' ability to stay calm.