Police said at a news conference in the city of Manaus that the prime suspect in the case detailed what happened to the pair who went missing on June 5.
The federal investigator, Eduardo Alexandre Fontes, said Amarildo da Costa de Oliveira, 41, nicknamed Pelado, told officers he used a firearm to kill the two men.
Fontes said the suspect took police to a spot on Wednesday where they recovered human remains.
The remains had not yet been positively identified, federal police said.
"We found the bodies three kilometres into the woods," the investigator said on Wednesday.
He said other arrests would be made soon in the case.
Another officer, Guilherme Torres of the Amazonas state police, said the missing men's boat had not been found yet but police knew the area where it purportedly was hidden by those involved in the crime.
"They put put bags of dirt on the boat so it would sink," he said.
As federal police announced they would hold a news conference, colleagues of Pereira called a vigil outside the headquarters of the Brazilian government's Indigenous affairs agency in Brasilia.
The Indigenous expert was on leave from the agency when he disappeared on June 5 while travelling with Phillips, a British freelance journalist and regular contributor to The Guardian newspaper.
Phillips' wife Alessandra Sampaio said in a statement that "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," she 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."
Pereira, 41, and Phillips, 57, were last seen on their boat in a river near the entrance of the Javari Valley Indigenous Territory, which borders Peru and Colombia. That area has seen violent conflicts between fishermen, poachers and government agents.
Developments began moving on Wednesday when federal police officers took a suspect they did not identify at the time out on the river toward search parties looking for the missing men.
On Tuesday, police said they had arrested a second suspect in connection with the disappearance. He was identified as Oseney da Costa de Oliveira, 41, a fisherman and a brother of Pelado, who police already had characterised as their main suspect.
De Oliveira told AP on Friday that he had visited Pelado in jail and was told that local police had tortured him in attempts to get a confession. Mr de Oliveira said his brother was innocent.
Indigenous people who were with Pereira and Phillips have said that Pelado brandished a rifle at them on the day before the two men disappeared.
AP with PA
