The 30-year-old became the first British driver to win back to back titles and also the first to win 10 or more races in successive seasons.
Hamilton's German team-mate Nico Rosberg, who started on pole, finished second after making a costly late mistake while leading.
Ferrari's Sebastian Vettel took third place a mere 0.5 of a second behind. Hamilton had needed to beat Vettel by nine points and Rosberg by two to take the crown, but for much of the race it looked as if he would have to wait at least until Mexico next weekend.
Hamilton had forced pole-sitter Rosberg wide at the first turn of the first lap, nipping through to take the lead, but the Red Bulls of Daniel Ricciardo and Dany Kvyat put the pressure on him.
Ricciardo moved through at one point and built an eight-second lead, but he could not hold off the power of the Mercedes cars. Rosberg reclaimed the lead for a while, but Hamilton forced him into an error eight laps from the end, as the German ran wide and lost pace, allowing the defending champion to hold on until the end.
Mercedes team-mates Nico Rosberg and Lewis Hamilton
Image credit: AFP
Although there was standing water on the track, the rain, which blighted much of the race weekend, stayed away, meaning unpredictable conditions and some hastily rejigged race tactics. There were also some spectacular collisions, notably Kvyat skidding over some artificial turf and skewing off into the opposite barrier wall, but emerging unharmed.
Manor Marussia's Alex Rossi was another driver delighted with his race - despite three incidents necessitating safety cars, both virtual and real, the American emerged unscathed at his home race.
Elton John interviews Lewis Hamilton after the US GP
Image credit: Reuters
Lap 1/56 - Hamilton pushes Rosberg wide and takes the lead on the opening corner - the cars touched but neither was damaged.
Lap 16/56 - Red Bull's Daniel Ricciardo overtakes Lewis Hamilton to take the lead - Hamilton pits soon after.
Lap 27/56 - With the Red Bulls struggling for grip. Nico Rosberg takes charge of the race.
Lap 43/56 - The safety car comes out after Daniel Kvyat puts his car into the wall.
Lap 49/56 - Mistake by Rosberg as he veers wide and Hamilton nips through into the lead.
Lap 56/56 - Lewis Hamilton is world champion!
Lewis Hamilton (Mercedes) - GP of United States of America 2015