Although the 20-year-old Mercedes driver finished third in the Mexican capital on Sunday (Monday AEDT), he became the youngest champion in Formula One history.
"Thank you so much, we did it, we did it, thank you so much ... thank you," Antonelli said on the team radio after securing the title with four races still left in the season.
Antonelli, the first Italian to win the title since Alberto Ascari in 1953, took an unassailable lead in the standings over teammate George Russell and Ferrari's Hamilton.
Sebastian Vettel was the previous youngest champion at age 23 in 2010.
Verstappen won the Mexico City GP for the sixth time.
"I would not be here without Mercedes and my family, I am speechless just trying to process this," Antonelli said at the end of the race. "It has been an incredible season."
Formula One chief executive Stefano Domenicali was another proud Italian and applauded his compatriot's achievement.
"For 73 years, our country has waited for this moment, and today an entire nation will celebrate one of its own reaching the very pinnacle of our sport," Domenicali said.
"Today, his name joins the legends of our sport.
"A new chapter in Formula One history has been written, and I firmly believe this is only the beginning of an extraordinary legacy."
The race was stopped on lap 46 with a red flag after Valtteri Bottas crashed into the wall at the first corner, following issues with his right-side suspension.
Cadillac reported that the driver was given "further medical assessments as a precaution".
Bottas had got out of the car unaided and waved to the fans before leaving the track.
At the restart, Verstappen was first - followed by Charles Leclerc, Hamilton, Antonelli, Lando Norris and Russell - and the Red Bull driver did not let the win slip away.
After Mexico, F1 will head to Brazil and then to Las Vegas. It remains uncertain whether the final two scheduled Grands Prix - in Qatar and Abu Dhabi - will take place, given instability in the region.
Hamilton, who had secured pole position on Saturday, lost it on the fourth lap while battling for the lead with Leclerc. Hamilton briefly went off track, dropping back to third place.
The manoeuvre between the two Ferrari drivers was investigated, resulting in a five-second penalty for Leclerc - a decision that left seven-time world champion Hamilton fuming.
"The stewards are basically handing Charles this win. We agreed in the drivers' briefing," Hamilton said.
"The problem with a five-second penalty is that he's got clean air and doesn't have to manage (the car) like the rest of us. He should have just given the position back."
Shortly before the red flag caused by Bottas's crash, Hamilton radioed, "We've got problems ... big, big problems."
On pulling into the garage, he appeared visibly frustrated with his team.
Despite his angst, Hamilton proved his class by forging to second place.
Australia's Oscar Piastri finished seventh in Mexico, two places behind his McLaren teammate and last season's champion Norris.
YOUNGEST FORMULA ONE WORLD CHAMPIONS
20 years 68 days (2026) Kimi Antonelli, Italy
23 years 133 days (2010) Sebastian Vettel, Germany
23 years 300 days (2008) Lewis Hamilton, Britain
24 years 57 days (2005) Fernando Alonso, Spain
24 years 73 days (2021) Max Verstappen, Netherlands
25 years 273 days (1972) Emerson Fittipaldi, Brazil
