Scott Prince, 19, Louis Pymar, 18, and Debbie Hayes, 24, survived for more than 10 hours in the sea off Fiji after a ferry broke apart and capsized.
The three were among 23 passengers on board when the overloaded boat sank on Monday evening. There were only 15 lifejackets available and darkness was falling.
The 30ft boat, which was carrying a mixture of British, Irish, Swedish, New Zealand, French, Israeli and Canadian passengers, was travelling between the island of Tavewa and the main island of Viti Levu when it sank. All the passengers and crew survived.
After several hours clinging to the wreckage of the boat, the three Britons decided to swim ashore with 10 others. They reached a deserted island where they drank from coconuts before being picked up by a passing cruise ship.
The three Britons looked fit and healthy, although slightly overwhelmed by the reunion with their families. Mr Prince, from Feltwell, Norfolk, who lost all his belongings, said: "The whole thing happened so quickly. We were trying to think when we would get rescued and we tried to all stay strong.
"We were in the water for five hours and then around 13 of us decided to swim. It was another four to four and a half hours before we reached shore."
The dreadlocked teenager said that when the group finally reached the island "we collapsed through exhaustion".
"No one could get any sleep that night and we tried to keep as warm as we could until we got picked up," he said.
His childhood friend, Mr Pymar, from Mundford, Norfolk, who had been on the round-the-world trip with Mr Prince since November, said the group managed to stay together during their arduous swim because they had devised a number system to keep track of everyone.
Mr Pymar, who is due to start a university course in October, said: "We all had a number from one to 14 and kept calling them out through the night." The group decided to exclude the number 13.
"It was important in the dark to stay together. We were looking to the stars for guidance and the islands to help us," he said. When they were picked up by a passing cruise ship, the Nanuya Princess, "everyone just broke down in tears".
Standing between her new-found friends, Ms Hayes, who had been travelling alone since January, said: "I will never forget the number three for the rest of my life."
She was met at the airport by her mother, father and tearful sister. Before taking her home, the family, from Weybridge, Surrey, planned to take her to a doctor for treatment to her feet: they had been severely cut on the island's coral.
Mr Prince, referring to the lack of safety gear on the ferry, said: "I hope something is done about the situation. Unless this happens, tragedies like this will continue."Reuse content