The 31-year-old from Fenwick had been missing since Saturday, 19 December, 2020.
His next of kin has been notified.
His death is being treated as unexplained, pending a post mortem examination.
A report will be submitted to the Procurator Fiscal.
Chief Inspector Nathan Calderwood, East Ayrshire area commander, said: "Our thoughts are with Jackson's family and friends at this difficult time.”