Francis Dellipiani, known as Frank, vanished from his home in Estover on New Year’s Eve.
Police in Kingsbridge say a body was discovered in the Derriford area of the city on Saturday morning.
His next of kin have been informed.
The 62-year-old's disappearance sparked a major rescue operation led by specialist officers from the South Hams.
Kingsbridge Police said: “Searches continued on Saturday, January 4, for the missing man, Francis “Frank” Dellipiani.
“Regrettably, the body of a man was discovered within the search area.
“Although no formal identification has taken place, the family of Francis Dellipiani, known as Frank, have been informed.
“Our sincere condolences go out to his family and friends and our sincere thanks to all the agencies who assisted in the searches.”
A Devon and Cornwall Police spokesperson said: “Police searching for 62-year-old Francis Dellipiani, who was reported missing from the Estover area of Plymouth, have found the body of a man.
“The body was located near to the Brest Road area at around 11am on Saturday, January 4.
“The family of Mr Dellipiani have been informed of the discovery.
“The death is not being treated as suspicious and a file is being prepared for the coroner.”