It was not yet clear how many bodies the graves contained, a police lieutenant colonel said, adding that the victims had been executed by the Islamic State jihadist group.
The three sites are in the Saqlawiyah region, north of Fallujah, in the Karma area, east of Fallujah, and behind the old central library in central Ramadi, the province's capital.
Ramadi lies about 100 kilometres (60 miles) west of the Iraqi capital Baghdad, and Fallujah is located half-way between the two.
He said there appeared to be several dozen bodies in the three graves but added no definitive number was yet available.
Security forces were deployed to protect the site and forensic teams from Baghdad were expected in the coming days, he said.
Ammar Nuri al-Dulaimi, an official from the Martyrs Committee for Anbar province, said the discoveries were the result of an investigation by a purposely formed investigation team.
He said preliminary findings showed that some of the victims had been shot in the head, suggesting they were executed by IS.
IS fighters carried out several spectacular attacks on military bases in the area in 2015, in some cases capturing large number of soldiers and executing them.
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