Angela Glover, from Brighton, died after an undersea volcano erupted near the Pacific nation on Saturday, sending large tsunami waves crashing across the shore.
Her brother, Nick Eleini, said the 50-year-old died while trying to save her dogs.
He believes her body was found by her husband James in some bushes and the family discovered she had died at around 7am on Monday.
Her family and friends appealed for information on her whereabouts after she went missing at the weekend. They said in Facebook posts Mr Glover held on to a tree while Mrs Glover and her dogs were washed away.
Reading out a statement, her brother told Sky News: “I understand that this terrible accident came about as they tried to rescue their dogs.
“Angela and James loved their life in Tonga and adored the Tongan people. In particular, they loved the Tongan love of family and Tongan culture.
“From a little girl, it was always Angela’s dream to swim with whales, and it was Tonga that gave her the opportunity that allowed her to fulfil these dreams.
“As you can imagine, her family is devastated and we respectfully request that we are given privacy to grieve.”
He said the couple moved to the nation after they got married in 2015 and they had become “well loved” locals.
Mrs Glover ran an animal rescue shelter in the country, called the Tonga Animal Welfare Society (TAWS), while her husband owns a tattoo shop, called the Happy Sailor Tattoo Parlour in Nuku’alofa, the country’s capital.
Mr Eleini said he and his mother had last seen Mrs Glover prior to the Covid-19 pandemic when they visited the UK.
He added: “This is just a terrible shock that it’s happened. We’re ordinary people, stuff like this doesn’t happen to people like us.
“She was beautiful, she was a ray of sunshine. She would walk into a room and lighten the room up. She loved her life. She was working in London and then achieved her life’s dream of working in the South Pacific. She loved her life there.
“She was just a lovely girl. She was the centre of our family and we’re just broken.”
Speaking to the BBC later on, Mr Eleini described his sister as “irreplaceable”, adding: “I had a strong bond with her. We loved each other dearly. She came to see us in our home in Sydney quite often. I’ve got three daughters and they just loved her so much. They, too, are just beyond grief.”
Foreign Secretary Liz Truss tweeted: “My thoughts are with those caught up in the appalling devastation and loss of life caused by the tsunami in Tonga. The UK stands ready to help the recovery effort and we are working closely with the Tongan authorities.”
New Zealand and Australia have despatched military surveillance flights to assess the damage.
New Zealand’s prime minister Jacinda Ardern told a press conference on Sunday power had been cut to the island as a result of the tsunami, while an ash cloud has contaminated water. She added defence forces were working to get water and supplies to citizens.