Nico Rosberg appeared on course to postpone his team-mate’s title celebrations for one more race, but the German made an unforced error with just seven laps remaining to allow Hamilton to take the lead.
Sebastian Vettel fought his way back from 13th to finish third in one of the best races in recent memory but it was not enough to prevent Hamilton from amounting an unassailable lead in the championship with three races to spare.
Hamilton joins Ayrton Senna and Jackie Stewart with three titles to his name. An emotional Hamilton struggled for words inside his crash helmet after he was informed he had seen off Vettel and Rosberg to win this year’s crown.
“This is the greatest moment of my life,” he said over the team radio. “To my family, I love you all.”
Hamilton needed to outscore Vettel and Rosberg by nine and two points respectively to win the title here in Austin — but the Briton appeared to have his work cut out after Rosberg secured pole in Sunday’s rearranged qualifying session.
Hamilton started alongside his team-mate but after a blistering start in the damp conditions, he muscled his way past the German on the long uphill run to turn one.
In a scene which summed up his faltering season, Rosberg was left trailing on the run-off area and both Red Bulls of Daniil Kvyat and Daniel Ricciardo as well as the Force India of Sergio Perez went by.
At first glance it appeared a fair move by Hamilton on his Mercedes team-mate but on further inspection the pair appeared to bang wheels with the Briton leaving Rosberg little room for manoeuvre.
Rosberg fought his way back past Perez on the opening lap but he was still only fourth. In the testing conditions Fernando Alonso and Felipe Massa also made contact at turn one. Alonso sustained a rear puncture and Massa eventually retired.
Back up front, Hamilton led but he was failing to shake of Kvyat and Ricciardo who appeared to be revelling in the wet conditions.
Hamilton struggled as the track began to dry out and on lap 15, Ricciardo, now in second, made his move. Within two laps, the Australian had pulled out a four-second lead over Hamilton, and on lap 18, it was Rosberg’s turn to make his way past the Briton. Hamilton dived into the pit-lane and was first of the leaders to take the dry tyre. It was a bold call, but after Ricciardo, Rosberg and Kvyat all pitted on the next lap for slicks, it was the right one.
That said Hamilton was now only fourth before Mercedes displayed the form which has seen them dominate the sport for the past two seasons. On lap 22 Rosberg sailed past Ricciardo for the lead and moments later Hamilton eased his way around Kvyat to move up to third. Incredibly Vettel, who had started in 13th after a 10-place grid penalty, was fourth after passing Kvyat.
On lap 26, Hamilton muscled his way past Ricciardo to move up to second but he was now 10 seconds behind race leader Rosberg. A safety car deployed after Ericsson’s Sauber stopped on track wiped out Rosberg’s lead.
Rosberg retained his nerve at the restart to stay ahead of Hamilton – but moments later Nico Hulkenberg and Ricciardo collided and the safety car was deployed. Rosberg dived in for a new set of tyres but Hamilton did not, which meant the Briton now led a topsy-turvy race.
The safety car was out once more on lap 43 after Kvyat crashed into the pit wall. Hamilton pitted and Rosberg retook the lead. The German looked set to win, and deny Hamilton victory and the championship, but he locked up his rear tyres, ran off the track, and Hamilton sailed by with just seven laps to go.
Hamilton went on to win his 10th grand prix of the year, and with Vettel who finished only half-a-second behind Rosberg in third, it meant the championship was his.