Mountain rescue search teams made the discovery in a wooded area close to the estate in Bakewell on Saturday morning.
Derbyshire Police said they believe it to be that of Youlgrave man Robert Graham Moore, who had last been at Sainsbury’s in Matlock on Sunday, June 16, at 1.30pm.
In a statement, police said: “Formal identification is yet to take place but Mr Moore’s family have been informed. Our thoughts are with them at this sad time.
“Officers do not believe there to be any suspicious circumstances surrounding the death and a file is being prepared for the coroner.”