The 26-year-old Norris became the first British champion since Lewis Hamilton in 2020, and he also denied Verstappen a fifth straight title.
Norris entered the three-way battle 12 points ahead of Verstappen and 16 ahead of Piastri.
Verstappen started from pole position for Red Bull with Norris on the front row beside him and Piastri third on the grid. Verstappen needed Norris to be fourth or lower and Norris had to finish outside the top five if Piastri won.
Verstappen's astounding late-season charge came close to unseating both McLaren drivers after they had shared the lead throughout the season and then were undone by driver and team-strategy errors.
But even Verstappen's season-leading eighth win and 71st of his career could not stop Norris, who kept his composure on Sunday having been under severe pressure in recent weeks.
The McLaren motorhome erupted with joy and CEO Zak Brown congratulated Norris on the team radio in his usual jovial manner.
“Lando, this is Zak from McLaren. Is this the world champion hotline? You did it! You did it! Awesome," Brown said.
Norris didn’t know whether to laugh or cry. He did both.
“Oh my God, thanks so much. I love you guys. Thanks for everything,” Norris said and then broke down in tears.
After crossing the line, Norris stayed in in his car for a few moments, visibly emotional. His parents were on the side of the track and he went over to hug them before celebrating with his McLaren engineers and mechanics.

