Having survived on nothing but coconuts, water trapped by a tarpaulin and a seabird that landed on their small vessel, the boys were reported to be dehydrated and badly sunburned but otherwise unscathed.
The teens, who hail from Tokelau Islands, a New Zealand territory in the south Pacific, had gone missing in October. Intense searches for them and their boat turned up nothing, leading their loved ones to assume they'd perished at sea.
In an interview with Radio New Zealand, Tai Fredricsen, first mate of San Nikunau, the tuna vessel that spotted the teens, said they were now aboard his ship, listening to music and watching cartoons.
"In the physical sense they looked very physically depleted," Fredricsen told Radio New Zealand but said their spirits were high as they repeatedly thanked their rescuers.
Samu Perez's aunt told the BBC after her nephew's rescue that the boy's family had already held a memorial service for him.
"My mum, she cried very day and every night," Fekei said. "We believed he was still alive anyway. We thought that God was still with them."
The woman told the BBC that the teens may have been trying to sail to Australia or the United States. She has spoken by phone with Perez, she told the BBC, and said he was asking for forgiveness.
"I think they did learn a big lesson," she said.
The boys told the tuna vessel workers that after losing their way during a sporting event, they used the nightly rains to catch drinking water, Fredricsen told the radio station. But during the past two days of their ordeal, they were forced to drink seawater, which rapidly dehydrated them.
"They said they had last eaten almost two weeks prior to us rescuing them," Fredricsen said, relaying how the boys described to him catching and killing a seabird.
Fredricsen said he told the boys they were smart to eat the bird rather than trying to catch fish, which would have further dehydrated them.
Once onboard Fredricsen said he and his crew were careful to give the boys just small amounts of liquid at a time to prevent them from becoming ill, and then small amounts of food such as pieces of an apple.
The tuna vessel was en route to Suva, the capital of Fiji, where the boys are expected to be hospitalized, Radio New Zealand reported.
Fredricsen called the rescue "very morale up lifting" and noted that the boys were found in an area that sees little to not boat traffic. Even Fredricsen's boat rarely travels that way but did this time.
"There's a lot of living left in them," he told the radio station.