It is Norris' first F1 title, which Verstappen has dominated over the last four years.
The Briton pipped his Red Bull counterpart by just two points to clinch the crown, with Piastri trailing the pair in third in the final standings.
Norris’ triumph makes him McLaren’s first world champion since Lewis Hamilton in 2008, and only the 11th British driver ever to win the title.
Ferrari's Charles Leclerc took fourth in Abu Dhabi while Mercedes' George Russell finished in fifth.
"I haven't cried in a while. I didn't think I would cry, but I did," Norris said on the podium after the race.
"I want to thank my mum, my dad, they've supported me since the beginning.
"It feels amazing, I know now what Max feels like a little bit. I want to congratulate both Max and Oscar. I've enjoyed it, it's been a long year," he added.
McLaren, headed by team principal Andrea Stella and CEO Zak Brown, secured back-to-back constructors' titles in Singapore last month.
"That was exciting, a little too exciting, awesome," said Brown.
Sunday's season-closer was the first time since 2010 that more than two drivers went into the last race with a chance of winning the title.