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.
Police have confirmed that a body found on a Fife beach was that of a missing 43-year-old woman.