Gregorio De Leo, from Biella Betulle, in Piedmont, had led for much of the fourth and final round as he sought to keep the crown in Italian hands following the 2017 victory of compatriot Andrea Romano.
But Brown – who had trailed by two shots going into the fourth day and by three at the turn – denied him with his stunning finish.
He also ended the hopes of Finland’s Eemil Alajarvi, who had strung together a run of five birdies in eight holes from the ninth to threaten.
Alajarvi matched the Hallamshire player’s birdie at the last to take third place behind De Leo.
Brown had begun with a one-over-par 73 in which he only struck the ball on 67 occasions, the other six shots being penalty additions.
He followed with consecutive scores of four-under-par 68 and closed with a one-under-par 71.
De Leo started round four with a birdie to stretch his advantage to three, which he maintained as he reached the turn in level and Brown in one over.
The Yorkshire teenager closed the gap to two with a birdie at 11 and was then breathing down the Italian’s neck when he bogeyed 12. But Brown repaid the favour with a dropped shot at 13 to stand two adrift with five holes to play.
That advantage was halved again when De Leo had his fourth bogey of the day at the 15th and while he parred his way in Brown had a three at 17 and a four at 18 to lift the trophy.
The 17-year-old struggled with a wayward driver, but pulled off some outrageous shots from thick rough, under trees and in bushes to keep himself in the running.
“I knew I had a good chance,” said Brown, after pulling off his win. “But I completely lost my game. I just got up and down from all over place and my putter saved me. I aimed to stay in it as long as I could and hope it would come good at the end, which it did.
“It’s nice to do it, especially here in Yorkshire in an England Golf event.”
The 17th was the turning point for Brown. He rammed home a 35-footer for birdie and into a tie for the lead after De Leo was unable to follow him in on the same line.
“A few putts had just slipped by because I hadn’t hit them hard enough,” said Brown. “On that one, I thought it was time and I gave it a bit more pace. I knew Gregorio was right on my line and I would give him a good read, so I knew I needed to hole it.”
On the last, Brown put himself in a great position off the tee and his second finished pin high, just off the green. De Leo, meanwhile, hit his drive into a bunker and reached the green in three. Brown chipped dead for a certain birdie and the Italian’s attempt to force a play-off slid by.
“I was nervous over that chip,” said Brown. “Definitely.”
Brown also helped England win the Nations Cup, teaming up with Harrison Arnold (Castle Royle) and Enrique Dimayuga (Walton Heath). Their team total over 36 holes was eight under par and they finished six shots ahead of Italy.
The Carris Trophy winner also claimed the Malcolm Reid Salver for the best aggregate score in the Carris and Peter McEvoy Trophies.
Rotherham’s Ben Schmidt carried on his from from last week’s McGregor Trophy – the English Boys’ Under-16 championship in which he came second – by finishing seventh at Fulford.
He had four back-nine birdies on the last day and carded rounds of 76 67 71 71.
Rotherham’s Charlie Daughtrey (75 73 73 76) played his last 10 holes of the week in three under.
Woodsome Hall’s George Heath (75 73 75 77) had two birdies in his last three holes while Fulford’s George Robson (71 76 76 81) – the host club’s junior captain – put up an impressive showing, making the cut after being called up from the reserve list.