Alistair Wishart, of Lerwick, was last seen on Saturday evening.
Police launched an extensive search for the 74-year-old, deploying coastguard teams and a helicopter in the hunt.
Mr Wishart's family have been informed of the sad development. His body was discovered yesterday afternoon on the shoreline below Breiwick Road in Lerwick. When last seen, he was wearing a navy jacket, navy jogging bottoms and navy slip on canvas shoes.
A Police Scotland spokesman said: "Enquiries are ongoing to establish the circumstances surrounding Mr Wishart's death and a report will be submitted to the procurator fiscal."