Ian Carruthers, 31, was reported missing from the town of Annan in Dumfries and Galloway on January 17.
Police Scotland confirmed that a body discovered on the Solway Firth shoreline at Portling, near Dalbeattie, last Friday morning was that of Mr Carruthers.
The force said that a 25-year-old woman, from Annan, was arrested for allegedly wasting police time and 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.
A spokesman said: "Following full consideration, both the accused were liberated from custody pending further inquiries."