The remains of the woman were discovered at Monreith, near Newton Stewart, on Tuesday August 11.
Police Scotland have confirmed that the woman has been identified as 71-year-old Breda Delaney of Avondale Court, Blackrock, County Dublin in the Irish Republic.
Ms Delaney had been missing from her home since Saturday July 11.
A police spokesman said: “Family of the deceased have been made aware and the Procurator Fiscal has been notified.”
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