Their Jeep was found by the loch and subsequent searches of the shoreline led to the recovery of a body on Wednesday evening.
The boat used by the fishermen was located nearby but the second man remains missing.
Inspector Alicen Winston said: “Police inquiries are at an early stage in what appears to be a tragic accident where one male has died and another remains missing.
“Agencies responding to the report of the missing men have been greatly assisted by members of the local community and I thank them for their assistance with our efforts to trace both men.”
A coastguard helicopter from Sumburgh and fire and rescue crews were drafted in to assist the search for the men from the Dounby area, who have not yet been identified.
A spokesman for the Scottish Fire and Rescue Service said: “We were alerted by police at 1.34pm to reports that the men, who were believed to have been fishing the area around Loch of Boardhouse, had not been seen for some time.
“We sent two fire and rescue crews from Stromness who assisted police and coastguard personnel.”