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.
Mr Phillips, 57, and Mr Pereira, 41, disappeared in a remote part of the Amazon rainforest on 5 June.
Two suspects, brothers Amarildo and Oseney da Costa de Oliveira, have been arrested in connection with the case.
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, and the motive for the killings is under investigation.
Detective Eduardo Fontes said the suspect “pointed out the place where he buried the bodies”.
Mr Phillips’ wife, Alessandra Sampaio, said in a statement: “Although we are still awaiting definitive confirmations, this tragic outcome puts an end to the anguish of not knowing Dom and Bruno’s whereabouts. Now we can bring them home and say goodbye with love.
“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.”
She expressed her thanks to everyone involved in the search for her husband and Mr Pereira, “especially the indigenous peoples and Univaja”.
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.”
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 involved a huge amount of work to get to the location that the suspect had indicated.
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 the 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 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.
Days before Mr Phillips and Mr Pereira went missing, indigenous groups say Mr Pereira was threatened for campaigning against illegal fishing in the area.
Some of their belongings, including clothes and a laptop, were found on Sunday.