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 said her body was found by her husband James.
Reading out a statement, he told Sky News: ‘I understand that this terrible accident came about as they tried to rescue their dogs.
‘As you can imagine, her family is devastated. And we respectfully request that we are given privacy to grieve.’
An undersea volcano erupted near the Pacific nation of Tonga on Saturday, sending large tsunami waves crashing across the shore and islanders rushing to higher ground.
The eruption has prevented international communications to the island, leaving friends and family members around the world anxiously trying to get in touch with loved ones.