Detective Eduardo Fontes said the man, Amarildo da Costa de Oliveira, nicknamed Pelado. took investigators to a site where human remains were dug up and told officers he used a firearm to kill the two men.
Police said at a news conference in the city of Manaus that the prime suspect in the case confessed and detailed what happened to the pair who went missing on June 5.
“We would have no way of getting to that spot quickly without the confession,” Mr Fontes said of the place where police recovered human remains on Wednesday after being led there by Pelado.
The investigator added that the remains are expected to be identified within days, and if confirmed as the missing men, “will be returned to the families of the two”.
“We found the bodies three kilometres (nearly two miles) into the woods,” he said, adding that rescue teams travelled about one hour and forty minutes on the river and another 25 into the woods to reach the burial spot.
Pelado’s family had said previously that he denied any wrongdoing and claimed police tortured him to try to get a confession.
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 Mr 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 Mr Phillips, a British freelance journalist and regular contributor to The Guardian newspaper.
Mr Pereira, 41, and Mr 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.
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."
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.
An Associated Press photographer in Atalaia do Norte, the city closest to the search zone, witnessed police taking the suspect, who was in a hood.
Indigenous people who were with Mr Pereira and Mr Phillips have said that Mr da Costa de Oliveira brandished a rifle at them on the day before the two men disappeared.