Forensic investigators made the identification on Friday after the prime suspect of Brazilian police confessed to killing Mr Phillips and his travelling companion, indigenous expert, Bruno Pereira.
Earlier in the week, fisherman Amarildo da Costa de Oliveira, 41, had led officers to where he had hidden the bodies deep within the forest, according to the country’s authorities.
Writing on Twitter, she said: “I am very sad to hear confirmation Dom Phillips’s body has been identified.
“My thoughts are with his family. I am grateful to everyone involved in the searches.
“We will continue to support Mr Phillips’s family, and the Brazilian authorities as the investigations proceed.”
Brazilian officers were continuing their hunt for the pair’s missing boat earlier on Friday, having said they had failed to locate the vessel despite “exhaustive searches”.
Investigators are still working to establish a cause of death, the country’s federal police said in their latest statement, and identification of Mr Pereira’s body has not yet been confirmed.
The remains were found last week near where the men disappeared on June 5 and flown into Brasilia on Thursday night following a 10-day search along the banks of the Itaquai river, according to Brazilian authorities.
Two arrests have been made in relation to the suspected murders, with police saying others may have participated.
Authorities have said a main line of the investigation has pointed to an international network that pays poor fishermen to fish illegally in the Javari Valley reserve, near where the men were last seen.
Officers earlier said da Costa de Oliveira, who police had been quizzing in connection with their disappearance, confessed to using a gun to kill Mr Phillips and Mr Pereira.
Investigators have not suggested a motive for the killing, but officials earlier said Mr Pereira’s work to stop illegal fishing in an indigenous reserve may have angered local fishermen.
In their latest statement issued on Friday night, Brazilian federal police said: “The confirmation (of Mr Phillips’ remains) was made based on dental examinations and anthropological forensics.
“Work is ongoing for a complete identification of the remains so we can determine the cause of death, and also the dynamics of the crime and the hiding of the bodies.”
The family of Mr Phillips, a long-time contributor to the Guardian newspaper and an environmentalist, said they were heartbroken.
In a statement issued through his brother-in-law Paul Sherwood on Thursday, the family said: “Early this morning we were informed that two bodies have been recovered from a remote location after a confession from one of the men in custody.
“We are heartbroken at the confirmation that Dom and Bruno were murdered and extend our deepest sympathies to Alessandra, Beatriz and the other Brazilian family members of both men.”
Friends and colleagues of the environmental campaigner also paid tribute, with some suggesting the deaths were the latest in a spate of attacks in the Amazon.
Greenpeace UK’s executive director Pat Venditti described the pair as “brave, passionate and determined men” who had carried out the “vital work of shining a light” on the daily threats Brazil’s indigenous peoples face in defending their land and rights.
Jonathan Watts, the Guardian’s global environment editor, said his long-time friend Mr Phillips had died in “an undeclared global war against nature and the people who defend it”.
In an opinion piece Mr Watts took aim at Brazilian authorities as well as the country’s president Jair Bolsonaro.
“The police refused to put a helicopter in the air after the two men were reported missing, and the military said it had the capacity to search but wasted more than a day while waiting for orders,” he wrote.
Mr Watts said the president, who earlier accused Mr Phillips and Mr Pereira of taking an “adventure” that was “ill-advised”, had “encouraged illegal logging and mining, dismissed indigenous land rights, attacked conservation groups, and slashed the budgets and personnel of forest and indigenous protection agencies”.