The Mercedes driver equalled the five titles of late 1950s Argentine great Juan Manuel Fangio.
Britain's Lewis Hamilton celebrated his fifth Formula One world championship after a Mexican Grand Prix won by Red Bull's Max Verstappen for the second year in a row.
The Mercedes driver, who equalled the five titles of late 1950s Argentine great Juan Manuel Fangio with only seven times champion Michael Schumacher ahead of them, finished fourth while Ferrari rival Sebastian Vettel took second place.
Hamilton, 33, had needed only five points to be sure of the title while four times champion Vettel had to win to have any hope of denying the Briton.
Ferrari's Kimi Raikkonen was third, meaning the constructors' championship remained open at least until the Brazilian Grand Prix in two weeks' time with Mercedes' lead trimmed.
In a nice sporting gesture, the Briton hugged Vettel and then ran back to the Mercedes garage to embrace his teammates one by one.
Australian Daniel Ricciardo, Verstappen's team mate, retired from the race with a smoking engine after starting from pole position.