Mr Corfield, 19, had not been seen since he left the White Horse pub in Builth Wells in the early hours of last Tuesday morning.
His body was found in the River Wye, Builth Wells, on Sunday afternoon.
In a statement, his family said: "We will miss James with all our hearts, and are utterly devastated."
Mr Corfield, a member of Montgomery Young Farmers' Club, was due to meet his family at the Royal Welsh showground where he had been camping with friends but failed to show up.
The statement continued: "James was very much a farming family guy - farming was his life, and he loved his animals with a passion.
"A visit to the Royal Welsh Show was a real highlight for him - and seeing the sheep and poultry judging was something he really looked forward to.
"He went to the Royal Welsh Show every year throughout his life, and we have fond memories of taking him as a child, which we will always treasure.
"We will miss James with all our hearts, and are utterly devastated. We are very grateful to all the volunteers who helped with the search, and for all the messages of support, but we ask now to be left in privacy."
Outside of farming Mr Corfield was a keen and "gifted" cricketer who played for Montgomery Cricket Club.
He was recently awarded Shropshire Division 2 Cricketer of the Year, and the league's young player of the year in 2016, which his family said was a "massive achievement for someone his age and something he was incredibly proud of".
A body found in the search for a man who went missing during the Royal Welsh Show has been identified as James Corfield.