RCCNZ mission co-ordinator, Conrad Reynecke, said the man was spotted waving his oars in the middle of a 4000 sq/km search area.
Speaking to the Herald from the wharf in 'Eua tonight, Veamatahau said he had had no food or drink for the past three days.
"Sunday, Monday, Tuesday - nothing,'' he said.
"No eat, no drink for three days.''
At some point, the father-of-two abandoned his fishing vessel for what he called a "small boat'' - the liferaft in which he was found today by rescuers.
In the severely hot sun, Veamatahau said it was the thought of his wife, Asela, and their young sons, 2-year-old Atalo and 5-month-old Tupouniua, that kept him going.
An emotional Asela Veamatahau told the Herald that, like her husband, it was the thought of her boys and her faith which kept her going also.
"It's so hard to explain. I didn't feel like doing anything at all. I had no strength.
"But then when I look at my boys, that became the only hope - and I trusted in God that my husband was okay.''
When told she her husband had been found alive, she broke down.
Family and friends of the couple quickly gathered at the wharf in 'Eua, where members of the Tongan Police delivered her husband safely back to them.
A doctor was on stand-by to look over Veamatahau, but a police officer said he appeared well and was in good spirits.
Asked if there was anything he would like to say to his rescuers, the keen fisherman became emotional - as did his wife.
"Thank you for all your help. Everybody who helped me. Thank you, thank you,'' he said.
Wife Asela also passed on gratitude to local authorities and particularly members of the NZ Defence Force who had answered a call for help.
