Detective Eduardo Fontes said the man, Amarildo da Costa de Oliveira, took investigators to a site where human remains were dug up.
He said police would work with Interpol to confirm the bodies’ identities.
In a statement, Mr Phillips’ family said they were “heartbroken” and thanked those who searched for the men.
Mr Phillips, 57, and Mr Pereira, 41, disappeared in a remote part of the Amazon rainforest that is rife with illegal poaching, mining and logging on 5 June.
Two suspects, brothers Amarildo and Oseney da Costa de Oliveira, have been arrested in connection with the case. It brings an end to a 10-day search that involved the army, navy and police.
Detective Fontes told journalists the “first suspect” – Amarildo – had “recounted in detail the crime that was committed and indicated the place where he buried the bodies”. His brother denies any involvement.
Police said they expect to carry out further arrests, adding that the motive for the killings was under investigation.
Mr Phillips’ family said in a statement: “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.”
“We are grateful to all those who have taken part in the search, especially the indigenous groups who worked tirelessly to find evidence of the attack,” it added.
Univaja, the region’s indigenous association, was the first to alert authorities when the pair went missing.
The group expressed its “deep sadness” following the news conference.
It said of the men’s deaths: “Univaja understands their murder is a political crime, they were both human rights defenders and died doing work to look after us indigenous people from Vale do Javari.”
Mr Phillips’ wife, Alessandra Sampaio, said: “Today, we also begin our quest for justice. I hope that the investigations exhaust all possibilities and bring definitive answers on all relevant details as soon as possible.”
It was a hastily-organised press conference – after another day of rumours that the bodies had been found.
The federal police officer in charge of the investigation showed a map to the waiting media – explaining that the bodies were found 3.1km (1.9 miles) from the river, in the middle of the jungle – and that it involved a huge amount of work to get to that location.
There was a great deal of praise for the joined-up efforts of all the armed forces – patting themselves on the back after a huge amount of criticism at the start that they hadn’t mobilised quickly enough.
They also initially failed to praise the work of the indigenous communities who have been out searching since the men disappeared, and helped lead authorities to some of their belongings found in the water. When asked by the BBC why there was no mention of the local communities helping, they admitted their support in working with the armed forces, with the head of the army in Amazonas explaining that many troops are indigenous in the force and that was crucial.
It might sound like a minor omission, but it reveals the divide between the bosses at the top here in the city – and the people living in these remote, difficult places.
Briton Mr Phillips, from Merseyside, had been living in Brazil for more than a decade and was a long-time contributor to the Guardian newspaper. He was working on a book about the Amazon.
Mr Pereira, a Brazilian who was on leave from his post with the government’s indigenous affairs agency Funai, was an expert on isolated tribes. He was introducing Mr Phillips to his contacts and acting as his guide at the time of their disappearance.
The pair went missing in the Javari valley, in Brazil’s far west, a remote region home to thousands of indigenous people from more than 20 groups. It is a refuge for these indigenous groups who live in isolation from the outside world.
But experts say the area has become a hotbed for crime due to its remoteness and a lack of government oversight. “What happened to Bruno and Dom is the result of an increase in organised crime, which is in turn explained by the absence of the state,” a former Funai official told the AFP news agency.
As well as clashes with poachers catching protected fish, it has also seen incursions by illegal gold miners, loggers and drug-traffickers who smuggle cocaine from nearby Peru and Colombia.
Violence has also grown as drug trafficking gangs battle for control of the area’s waterways to smuggle cocaine.
The region – which is about the size of Portugal – is known for violent conflicts between these various criminal groups, government agents and indigenous people. It was these conflicts that Mr Phillips and Mr Pereira were documenting.
And days before they pair went missing, indigenous groups say Mr Pereira was threatened for campaigning against illegal fishing. He had repeatedly reported being threatened by loggers, miners and illegal fishermen in the past.
Pat Venditti, the executive director of Greenpeace UK, praised the men as “brave, passionate and determined”.
“[They] were murdered while doing their vital work of shining a light on the daily threats indigenous people in Brazil face as they defend their land and their rights,” he said in a statement. “The greatest tribute we can pay Bruno and Dom now is to continue their vital work.”