The American's score of 568.65 was enough to beat China's Qiu Bo, who looked distraught to get silver with 566.85, while British pin-up Daley took bronze on 556.95.
Home favourite Daley found his groove on Saturday to ear-splitting cheers after he also had a lacklustre showing in Friday's heats.
"Although it's a bronze medal, to me it's a gold medal," said an ecstatic Daley, 18, who punched the air in triumph and jumped into the pool with his team after the result was announced.
"It's been a rollercoaster of emotions over the last few weeks but I've got an Olympic medal to show for it so I couldn't ask for anything more."
Boudia's gold marks a renaissance for the United States, who had not won an Olympic diving medal since 2000 but have also taken a silver and two bronze at London 2012.
Chinese teen sensation and world 10 metre champion Qiu, who has dominated the event since 2010 and was favourite for gold, hid his face on the pool wall when the result was announced and he realised that his back two and a half twisting somersault, the same dive Boudia performed last, earned fewer points than the American's.
"I just took it one dive at a time," said Boudia, 23, who had come within a whisker of dropping out in the preliminaries after qualifying last. "I was so calm, so at peace."
From the heats onwards, the men's 10 metre contest was outstanding for the quality of dives across the field, with no room for even the slightest error and big names such as Australia's Beijing gold medallist Matthew Mitcham failing to qualify for the final.
With Russia taking gold in the men's 3 metre springboard, Qiu's silver means China have lost out on two of the eight golds they had been aiming for in London.