Officers said the family of 88-year-old James Mainland has been informed after the find in the Birsay area.
Mr Mainland was reported missing from his home on July 7.
Chief Inspector Matt Webb said: “Our thoughts are with Mr Mainland’s family and the local community at this very sad time.
“I would like to thank residents and our partners in the emergency services for their support during searches for Mr Mainland.
“A police presence will be visible in the Birsay area over the course of today to allow us to establish the full circumstances which have led to this death.
“I would like to thank the community for their patience while this is ongoing.”