Hamiton was overtaken by Bottas in the closing stages of the 56-lap race at the Circuit of Americas in Texas with Red Bull’s Max Verstappen taking the final spot on the podium.
Hamilton’s 10th victory of the season in Mexico last weekend had left him needing just four points to achieve an unassailable lead in the standings and he duly delivered.
“What an incredible weekend, I can’t believe it, I really can’t believe it,” said Hamilton over race radio at the finish of a punishing race.
Only Michael Schumacher with seven world titles stands ahead of Hamilton, who has moved ahead of the legendary Juan Manuel Fangio in the all-time list.
Bottas, who started from pole, with Hamilton only fifth on the grid, was winning for the fourth time this season, hitting the front for the final time with three laps to go to complete a fine victory, the seventh of his career.
“It’s a good win,” said the Finn. “Personally, I failed on my target this year, but Lewis deserves it. He’s had a good season.”
Mercedes gambled on a one-stop pit strategy for Hamilton, but with fading tires he was unable to hold off the charging Bottas and was hanging on for second spot from Verstappen at the finish.
But it mattered little as he clinched his third straight championship with two races of the season left and to move within touching distance of Schumacher.
“It is overwhelming if I am honest,” said Hamilton. “I feel so much emotion. “I was pushing as hard as I could today and I was hopeful I could win but I didn’t have enough left in the tires.”
Hamilton was adding the 2019 title to previous triumphs in 2008, 2014, 2015, 2017 and 2018 and at 34 years of age shows little sign of letting up.
“I don’t know about how many championships I can win, but as an athlete I feel as fresh as I could be. We will keep pushing,” he said.
Sunday’s race proved another difficult afternoon for Ferrari, with both their cars dropping back at the start as they struggled for grip.
Sebastian Vettel was brilliantly overtaken by Hamilton, who also made his way past Charles Leclerc into third place in the opening flurry of activity.
Vettel eventually retired with broken suspension, while Leclerc finished a distant fourth, not the way Ferrari team boss Mattia Binotto wanted to celebrate his 50th birthday.
Alex Albon finished fifth in the second Red Bull with Daniel Ricciardo in sixth for Renault.
Hamilton has two more races this season in Brazil and Abu Dhabi to add to his career tally of 83 wins and to close on the all-time record of 91, held by ex-Ferrari ace Schumacher.
But with the remarkable consistency of his team, which has seen him finish in the points for 31 successive races and to take his tally of podium finishes to 150, few would back against Hamilton from surpassing all the records in a career that started in 2007 with McLaren, taking his first world title with them a year later.
“Lewis is still very motivated and you can see he wants to win every single race,” said Mercedes team principal Toto Wolff.
“As long as that is the case, he can go for more. We need to provide him with a good car. There is no limit.”