Lewis Hamilton has been crowned Formula One world champion after winning the United States Grand Prix in the most dramatic of circumstances.

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 now joins his idol Ayrton Senna and Sir Jackie Stewart with three titles to his name. He also becomes the first British driver to successfully defend his Formula One crown.

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 eventually said over the team radio. "To my family, I love you all."

On his return to the pits, Hamilton leapt out of his Mercedes before running to his team. He then made his way up to the green room - the area before the podium celebrations - where the emotion of his incredible achievement reduced him to tears.

A dejected Rosberg sat slumped in a chair in the corner of the room with Hamilton attempting to regain his composure by mopping down his brow.

Hamilton then threw a sponsors' cap for the podium in the direction of Rosberg, who responded by launching it straight back at his rival without so much as a hint of a smile.

The torrential rain which has plagued this weekend's action finally stopped in the hours leading up to the race.

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 morning'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, no doubt fuming by his team-mate's actions inside his crash helmet, 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. The former sustained a rear puncture and the latter eventually retired. Valtteri Bottas also damaged his front wing and retired on lap five while the Sauber pair of Marcus Ericsson and Felipe Nasr, on the team's 400th grand prix, collided with one another in a frenetic start to a frenetic race.

Back up front Hamilton led but he was failing to shake of Kvyat and Ricciardo who appeared to be revelling in the wet conditions. Rosberg was joining in the party, too and it was not long before the German and his Red Bull rivals were trading positions

Hamilton then 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 immediately dived into the pit-lane and was the first of the leaders to take on the dry tyre. It was a bold call, but after Ricciardo, Rosberg and Kvyat all pitted on the next lap for slicks, it proved to be 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 up to 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 this 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.