text: Media playback is not supported on this device
  Hamilton, 30, won a thrilling United States Grand Prix to seal the drivers' title with his 10th victory of 2015.
  He pressured team-mate Nico Rosberg into a mistake during a frantic last 10 laps after a safety car and swept by.
  It was an exciting climax to a race of fluctuating fortunes, lead changes and superb racing in changing conditions.
  Ferrari's Sebastian Vettel could have kept the race open until Mexico next weekend had he finished second, but could manage only third place behind Rosberg.
  "Amazing," Hamilton told singer Elton John during the podium interviews. "I can't find the right words to tell you how amazing this feels.
  "I love you guys and everything you do for me. For all my family, I love you all."
  Rosberg's error came a lap after a restart following one of two safety car periods in a race that also featured two interruptions by the virtual safety car.
  Media playback is not supported on this device
  Before that, the advantage had continuously swung back and forwards between the two Mercedes drivers in a race of fluctuating fortunes.
  With 15 laps to go, it appeared as if Hamilton was going to miss out, as he led the race but appeared a sitting duck with Rosberg on fresher tyres and closing in behind after stopping under a virtual safety car period while Hamilton stayed out.
  But then a heavy crash for Red Bull's Daniil Kvyat when the Russian lost control at Turn 19 gave Hamilton a lifeline when the actual safety car was deployed.
  He stopped for fresh tyres and rejoined in second place, right behind Rosberg, and the two were set up for an all-out battle for victory in the closing 10 laps.
  Now Hamilton had the advantage, on tyres eight laps fresher, and on lap 48 of 56 Rosberg lost traction out of the Turn 12 hairpin at the end of the long back straight, his car flicked from side to side and he ran wide off the track as Hamilton swept into the lead.
  The German tried to come back at Hamilton but the Englishman held him comfortably at bay.
  Hamilton was told he had won the title over the radio on his slowing down lap and initially struggled to speak, apparently fighting back tears, before managing to thank the team and his family for their support.
  He then performed donut spins for the fans in the stadium section towards the end of the lap before touring back to the pits for the ceremonies.
  Hamilton's team-mate Rosberg congratulated the Briton as they prepared for the podium interviews, but then appeared furious when Hamilton tossed a 'second place' cap towards the German, who then launched it back toward the champion.
  Rosberg said: "It has never happened to me ever something like that [the error], I can't explain it. I just need to look into it afterwards. It was really tough at the time to lose the lead like that and the win.
  "Turn One for sure was very aggressive [by Hamilton]. I haven't seen it so I can't comment until I have seen it. Extremely aggressive and we hit each other. Or I should say Lewis came into me, so that's not good. I can't say more than that."
  The race started on a wet track but with the sun finally breaking through after a weekend badly affected by rain on the periphery of tropical storm Patricia, which had forced qualifying to be held on Sunday morning.
  Hamilton immediately put himself in a position to win the title, making a better start from second on the grid behind Rosberg and taking the lead at the first corner, forcing his team-mate wide in the process and giving the Red Bulls of Daniil Kvyat and Daniel Ricciardo the chance to demote Rosberg to fourth.
  On a wet track on treaded intermediate tyres, the Red Bulls were faster than the Mercedes and Hamilton faced an initial attack from Kvyat.
  The top four were locked together for the first 19 laps as Rosberg moved into second, only for Ricciardo to pass him and then Hamilton to take the lead.
  Media playback is not supported on this device
  But once the track began to fully dry, the Red Bulls lacked the pace to challenge and dropped back and the race developed into a battle between the two Mercedes drivers.
  Hamilton initially struggled as Rosberg, driving what for a while looked set to be the best race of his career, took control.
  Hamilton began to push Rosberg hard after the first safety car period to recover a stranded car in the middle of the race, only for the virtual safety car to hand Rosberg what appeared as if it might be a decisive advantage.
  Rosberg pitted for fresh tyres just as the brief caution was poised to end and came out behind Vettel but on fresh tyres and with an apparently strong advantage.
  But then Kvyat's crash added a final twist and Hamilton sealed a title for which he has appeared on course since the very beginning of the season.
  Full United States GP results
  United States GP coverage details
target: Mercedes' Lewis Hamilton won his third Formula 1 World Championship to become only the second British driver after Sir Jackie Stewart to achieve the feat.