Police have formally identified the body found in the Port Hills on Monday as that of Shirley Warrington, who had been missing since early July.
The 85-year-old's death is not being treated as suspicious and the police will continue to make enquiries on behalf of the coroner.
In a statement, her family say they are relieved she has been found and want to express thanks and gratitude to those who helped search for her.
A Facebook page - Search for Shirley - was set up to help co-ordinate the on-going searches.
The family say the care people have shown will always be greatly appreciated.