Maureen Bannister, from Leuchars, had not been seen since about 14:00 on Sunday. It is thought she had been walking her dog in the area of Tentsmuir Forest in north-east Fife.
On Monday evening, a body was found on Tentsmuir Beach by a member of the public.
Police have said Ms Bannister's death is being treated as "unexplained".
Sgt Gary Combe said: "Our sincere condolences go to Maureen's family and friends at this very sad time.
"We're working to establish the full circumstances surrounding Maureen's death and are asking anyone who may have seen her since Sunday afternoon to get in touch."
Anyone with information is asked to contact Police Scotland on 101.

The 24-year-old, who has 26 caps for his country, has signed a deal, subject to a medical, until May 2018.
Sarto said: "Glasgow Warriors are a massive club and play a great style of rugby.
"I wanted to move to the UK as I know the standard of rugby is high and I want to improve my game. Joining a club like Glasgow will help me do that."
Sarto knows Warriors well, having played against them for Zebre in the Pro12, and scored a try when making his international debut against Scotland in the South African Quadrangular Tournament in 2013.
"I've always known Glasgow is a great club and I know Simone Favaro is enjoying it there," he said of the 27-year-old back-row forward.
"I hear the fans love him and I hope I will have a similarly good relationship with them when I move over."
Glasgow head coach Gregor Townsend said Sarto was a player Warriors "had been tracking for a while".
"Leonardo has been one of the best wingers in the Guinness Pro12 over the past few seasons and has an ability to break tackles," he added.
"He has also performed well at Test level and had an excellent all-round game against Scotland last month.
"We believe that he will make further improvements in our environment and will add to the competition for places in our backline."
Police have confirmed that a body found on a Fife beach was that of a missing 43-year-old woman.
[NEXT_CONCEPT]
Italy wing Leonardo Sarto has agreed to join Glasgow Warriors on a two-year contract in the summer from Zebre.