The 31-year-old held his nerve at the last to score a brilliant 97.75 points and snatch the title from Japan's Ayumu Hirano, who was leading on 95.25, with Australia's Scotty James third on 92.00.
It was particularly satisfying for White, known as "Flying Tomato" because of his red hair, who won gold in 2006 and 2010 and helped put the hipster sport on the map, but flopped in Sochi four years ago.
White said it had been an agonising wait for his score from the judges to come through, as he pipped Hirano to the title to make US history.
"Oh man, that was awful and amazing at the same time. I knew I did a great ride and I was proud of that and I could walk away with my head high, but when they announced my score and I'd won, it crippled me," he said.
"I was so overwhelmed with happiness, I've been through so much to get here. I had this crazy injury in New Zealand (in October) where I busted my face open.
"I actually did the same trick that injured me here in the halfpipe today. So there were a lot of obstacles to overcome and now it's all worth it."