Police said the death of Ian Carruthers, 31, had "all the hallmarks of a tragic accident".
Mr Carruthers was reported missing from the town of Annan in Dumfries and Galloway, on January 17.
His body was discovered on the on the Solway Firth shoreline at Portling, near Dalbeattie on Friday.
Police Scotland said that a full forensic examination and post mortem have proved to be "inconclusive" on the cause of death.
Detective Inspector Filippo Capaldi, of Police Scotland's Major Investigation Team, said: "Following extensive and exhaustive enquiries, there are no apparent suspicious circumstances in respect of the death of Ian Carruthers.
"Following the post mortem examination, the cause of death will remain recorded as 'unascertained', however, given all of the known circumstances and in the absence of any evidence to the contrary, his death has all the hallmarks of a tragic accident.
"I have spoken with Ian's immediate family and fully explained all of this to them, which will hopefully provide some closure for them in this matter."
Yesterday police said that two people had been arrested following the discovery of Mr Carruthers' body.
The force said that a 25-year-old woman, from Annan, was arrested for allegedly wasting police time and that a 26-year-old man, from Longtown in Cumbria, was arrested over alleged drug supply offences.
They were due to appear at Dumfries Sheriff Court yesterday but the Crown Office said both had been freed pending further inquiries.