Margaret Ann Llewelyn, 53, was last seen at her home in Chepstow in 2002.
Her disappearance prompted a major search operation and relatives made several appeals.
Gwent Police were called to Beaufort Quarry on 24 February and said the remains have been identified as the grandmother.
Human remains found at a quarry in Monmouthshire belong to a woman who had been missing for 14 years, police have said.