Crystalla Dean, 52, was last seen by her daughter at her home in Longsdale Crescent, Oban, at about 20:00 on 15 December.
On 5 January a body was found on the shore at Ardmucknish Bay near Benderloch.
Police said the body had now been formally identified as that of Ms Dean and her relatives had been informed.
Following a post-mortem examination, the death is not being treated as suspicious.
A large-scale search for Ms Dean took place, involving Police Scotland's mountain rescue team, the coastguard and the local mountain rescue team.
A body found in Argyll earlier this month has been confirmed as being that of a missing woman.