The family of Clive Colling - who disappeared from Bideford - has said that, subject to formal identification, he was found in the Torridge River on Friday.
A Facebook post said:"After 104 days nature finally gave him up."
Step-daughter Sally Hewins wrote: "Thank you to the locals for their thoughts, efforts and kindness."
She added: "He was found in the Torridge River by canoeists and I thank them for their bravery yesterday, along with the RNLI for the ultimate recovery and the police for their sensitivity."
The family held a candle-lit vigil for Mr Colling in Bideford on Friday evening.
Devon and Cornwall Police said formal identification would "confirm" the body's identity and "next of kin have been informed at this sensitive time".
A body found in a north Devon river is thought to be a 77-year-old dementia sufferer missing since New Year's Day.