Beamish is from a sheep and beef farm in Ongaonga and is a border at Napier Boys' High School.
His schoolmates Guy von Dadelszen, 15, and Macabe King, 15 took out second place.
"Hopefully competing at home will give us an advantage. We're really looking forward to it," said King.
Both teams will represent the East Coast in the FMG Junior Young Farmer of the Year Grand Final in Hawke's Bay.
"We're feeling pretty confident heading into the grand final. It's great that we know what to expect this time around," said Von Dadelszen.
Von Dadelszen and King also competed in last year's national final in Invercargill.
Abby Strang, 11, Stuart Addis, 12, and Chalkie Williams, 10, from Tikokino School won the fiercely-contested AgriKidsNZ contest.
That regional final saw 144 students, working in teams of three, take on a series of fun modules.
They included fitting tyres to a Honda quad bike, assembling a Hansen water system, a WorkSafe hazards challenge and correctly identifying different breeds of sheep and cattle.
Ben Gray, Sam Lawson and Rose Beamish, from Ongaonga School, placed second.
1st Finn Beamish and Matthew Halford. Napier Boys' High School 2nd Guy von Dadelszen and Macabe King. Napier Boys' High School 3rd Isabel Greville and Kaylee Hutchinson. Woodford House
AgriKidsNZ
1st Abby Strang, Stuart Addis, and Chalkie Williams. Tikokino School 2nd Ben Gray, Sam Lawson and Rose Beamish. Ongaonga School 3rd Harrison Brown, Sheldon Brown and Harry Bourke. Pahiatua School