Paul Dierikx was pulled from the Water of Leith yesterday (Mon) by specialist divers.
Two horrified workmen made the grim discovery at around 9.40am when removing debris that had gathered near the Victoria Bridge.
Police have today confirmed that the death is not being treated as suspicious.
A spokesman added that the Mr Dierikx was originally from Glasgow but had no fixed address.
He said that his family in Glasgow had been informed and a report is now being sent to the Procurator Fiscal.