Hamilton overtook his Mercedes teammate Nico Rosberg on the 49th of 56 laps at the Circuit of the Americas after a late safety car to clinch the championship. Sebastian Vettel, who also had a mathematical chance of denying Hamilton, finished third.
After a weekend hit hard by the affects of Hurricane Patricia, the spectators in Austin were rewarded with a topsy-turvy race, which looked set to fall to Rosberg until his late mistake allowed Hamilton through.
It is his 43rd career F1 victory, wrapping up the championship with three rounds remaining. "The greatest moment of my life" said an emotional Hamilton as he drew level with his boyhood hero Ayrton Senna for title victories and also matched fellow Briton Jackie Stewart.
Hamilton has won the championship for all-conquering Mercedes for the last two seasons, both times with Rosberg left in a supporting role.
His overtake on Rosberg to take the lead from second on the grid looked to have left him in control of the race, but he struggled for pace in changeable conditions and it looked as if he would have to wait until the Mexico round next week to clinch the crown.
But after Daniil Kyvat crashed in his Red Bull, the 30-year-old Hamilton was able to make a late pit stop to soft tires, negating an advantage which had been built up by his teammate.
It was still Germany's Rosberg to lose, but he ran wide to allow Hamilton to pass and came under late pressure from Ferrari's Vettel, holding second spot to ensure Hamilton would be crowned champion.
A crestfallen Rosberg, who had dominated for much of a race marked by safety car interventions, found defeat hard to take.
"Very disappointed. Unbelievable, I don't know what happened. Thanks to the fans, you've been awesome," he told pop star Elton John who made the presentations.
Four-time champion Vettel, who had to overcome a 10-place grid penalty and starting from the seventh row, finished quicker than anyone, serving notice of Ferrari's likely challenge to Mercedes next year.
Other notable performances in a race which started on a damp track after earlier downpours, came from teenager Max Verstappen in his Toro Rosso in fourth.
Jenson Button produced a fine drive for the under performing McLaren team in sixth, while American Alexander Rossi finished just out of the points in 12th place, while making his own piece of F1 history.
But all the focus was on Hamilton, who won his first title with McLaren before switching to Mercedes with such success. "I can't find the right words to tell you how amazing this feels," he told Elton John.