They say the identification was based on dental records.
The second body - believed to be that of indigenous expert Bruno Pereira - is still being examined.
Mr Phillips, 57, and Mr Pereira, 41, were first reported missing on 5 June. Earlier this week, a suspect confessed to burying the bodies.
The suspect was later named as Amarildo da Costa de Oliveira. The police said he had explained in detail how both men were killed before leading officers to the place where their bodies were buried.
