David Pleace, aged 57, from Derby, Orkney, was reported missing near Orkney on the afternoon of Sunday, 27 June.
A helicopter was deployed by the coastguard, as well as lifeboat teams from the area, to help with the search, while police officers also supported efforts to trace him.
However, a body was discovered yesterday, and police now say that they do not believe there were any suspicious circumstances surrounding the death.
Orkney Inspector David Hall said: "Police were made aware of the incident around 5.35pm on Sunday, 27 June.
"A multi-agency search response was launched and Mr Pleace's body was recovered on Monday afternoon.
"Our thoughts are very much with his family and friends at this extremely difficult time."
“There are no suspicious circumstances surrounding the death and a report will be submitted to the Procurator Fiscal in due course.”