Forensic investigators made the identification on Friday after the prime suspect of Brazilian police confessed to killing Guardian contributor Mr Phillips and his travelling companion, indigenous expert Bruno Pereira.
Local police have arrested three people over their deaths so far.
Latin America minister Vicky Ford confirmed on Saturday that the remains discovered were those of Mr Phillips.
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’ family, and the Brazilian authorities as the investigations proceed.”
Mr Phillips’ family earlier said they were heartbroken by his death.
On Saturday, his sister said he had been on his final of several trips in the Amazon this year, where he was speaking to people working on projects including sustainable agro-forestry.
Speaking on BBC Radio 4’s Today programme, Sian Phillips said: “I think he underplayed the risks to some extent.
“But we knew that there were risks.
“It was an area he had travelled in with Bruno before but of course things have changed since Bolsonaro has been in power.
“The rights of the indigenous people have been rolled back.”
Ms Phillips’ partner Paul Sherwood said the family is “almost certain” that the travellers were killed by people involved in illegal fishing because of their investigations into the trade and called for “justice”.
Speaking on the same programme, he said: “He (Mr Phillips) would have been aware that there would have been many people who would be happy to see the back of him because it was inconvenient truth he was uncovering.
“We are almost certain now that they were attacked by people who were involved in illegal fishing.
“What we don’t know is what lies behind that.
“Were they acting alone as the police have said recently or was there a larger involvement of other powerful people, organised crime?
“There is a lot of drug trafficking as well as organised crime involved in the poaching of fish.
“We want the kind of justice that makes it possible for journalists and protectors of the rainforest to feel that they are safe in continuing to report from and help the indigenous people.”
Authorities have also 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 pair were last seen.
The men disappeared on June 5 and indigenous communities and police launched extensive searches along the banks of the Itaquai river.
Ten days later, fisherman Amarildo da Costa de Oliveira, 41, led officers to where he had hidden the bodies deep within the forest, according to the country’s authorities.
The fisherman was arrested over their deaths, along with his brother Oseney de Oliveira, known as Dos Santos.
On Saturday, officers said Jefferson da Silva Lima, known as Pelado da Dinha, turned himself in to a police station in Atalaia do Norte in the Amazon.
Police said he will be referred to a custody hearing.
Identification of Mr Pereira’s body has not yet been confirmed.
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.”
Friends and colleagues of the environmental campaigner have 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”.