A body was pulled from the water at Newburgh on Monday.
The grim discovery was made shortly after 11am by a local man who was out on the river collecting logs.
He saw something floating among reeds and contacted police, who called in coastguard teams to recover the body.
It is understood the remains had been in the water for some time.
The Broughty Ferry RNLI lifeboat and St Andrews Coastguard Rescue Team were involved in the operation.
The man who found the body, who did not want to be named, said: “The body was floating in the reeds and I just reported it to the police.
“I wasn’t actually very sure what it was at first.”
The body was found near to where search teams had been looking for Bridge of Earn man William Rattray, 77, who went missing last month.
His disappearance was described as out of character and there has been mounting concern for his welfare.
Mr Rattray was last seen on Tuesday November 24.
His car was found abandoned in Bridge of Earn in the early hours of the following morning.
A police helicopter carried out a sweep of the surrounding countryside and members of the Tayside Mountain Rescue team joined firefighters for an extensive water search.
Investigators have also carried out door-to-door inquiries and searched back gardens and outbuildings around Mr Rattray’s home.
CCTV from businesses was also reviewed.
Local representatives in Newburgh had messages of condolence for the family of the man who had been found.
Howe of Fife and Tay Coast councillor David McDiarmid, who lives in the village, said: “I send my condolences to the family.
“There is never a good time, but this is probably the worst time of the year for anything like this to happen.
“Families are supposed to be preparing to enjoy a celebration, but this family will be thinking of other things.”
John Ferrans, the chairman of Newburgh Community Council, said: “This is a tragic thing to happen at any time of the year.
“Hopefully this will bring closure to the family.”
A Police Scotland spokesman said: “Police in north-east Fife attended at an area near East Shore Road, Newburgh, at around 11.25am on Monday December 21 following a report of a man’s body.
“Local officers and members of the coastguard were involved in the recovery of the body and inquiries are now ongoing to establish the man’s identity and the circumstances surrounding his death.”