Darren Gilpin, 29, was on Loch Tay on Saturday when his canoe capsized near the village of Killin.
A major search was launched and police said the body of a man was recovered last night.
A spokesman said: "Police Scotland can confirm that the body of a male person was recovered by police divers from Loch Tay near Killin. Investigations into the incident are still ongoing."
Mr Gilpin, from Edinburgh, was reported missing when his two-person canoe overturned at around 4.45pm on Saturday.
His companion managed to reach shore and raise the alarm, prompting a helicopter search.