Antony Hargreaves, 53, was reported missing to North Yorkshire Police earlier this month.
He was last seen by friends and neighbours on Thursday, September 6.
A man's body was found in the River Ouse shortly before 2pm yesterday (September 17) and although formal identification has not yet taken place, it is believed to be Mr Hargreaves.
A spokeswoman for North Yorkshire Police said: "The death is being treated as unexplained but there is not believed to be any third party involvement. A file will be prepared and passed to the coroner in due course.
"Our thoughts are with the family and friends of Mr Hargreaves at this sad time.
"Thank you to everyone who helped with the appeal to find Mr Hargreaves."
Police had earlier this month made a public appeal for information in an effort to find Mr Hargreaves.