A member of the public alerted the emergency services to the discovery at about 21:00 on Sunday.
Police Scotland said formal identification has still to take place, but that Mr Mitchell's family have been informed.
The 18-year-old was last seen in Inverness on 10 November on CCTV.
Searches were made of areas of Inverness, including along the shore of the nearby Moray Firth.
St Fergus, near Peterhead, is also on the Moray Firth coast.
The family of missing Inverness teenager Adam Mitchell have been informed of the discovery of a man's body near St Fergus in Aberdeenshire.