Denmark's Vingegaard of the Jumbo-Visma team crossed the finish line after the 21-day race, 7min 29sec ahead of Slovenia's Pogacar, the champion in 2020 and 2021.
Pogacar's UAE teammate Yates of Great Britain rounded out the top three podium.
The final stage was won by an outsider in Meeus of the Bora team, with Jasper Philipsen denied a fifth stage win on this Tour right at the line in a photo finish.
Vingegaard's winning margin was the largest since 2014 when Italian Vincenzo Nibali took the fabled champion's yellow jersey by 7min 39sec.
See the final standings on Flashscore.
The world's greatest bike race provided tense drama with spectacular backdrops as Vingegaard and Pogacar remained separated by seconds until the Dane edged ahead with a sensational individual time trial last Tuesday.
The following day, on a 28km climb to the ski resort of Courchevel, Pogacar cracked, shouting "I'm gone, I'm dead" before Vingegaard killed off the race with a sensational final climb.
The event had been billed as a showdown between the defending champion Vingegaard and Pogacar, who has won the Tour twice and now come second twice.
Tour director Christian Prudhomme used boxing terms to describe the struggle.
"They went 15 rounds and then there was a punch in the gut, a knee on the floor and a knockout punch," he said Sunday.
All-time great Eddy Merckx told AFP the pair had delivered a thrilling show.
"Pogacar is a more complete rider, but in the high mountains at least, Vingegaard remains the stronger," he said.
"I don't know what happened to me. I took on too much this year and after two weeks I started to look as white as this shirt," said runner-up Pogacar, pointing to his best under-25 rider's white jersey.
Pogacar started well enough, taking minor advantages in the Basque hills until Vingegaard attacked on the first mountain stage in the Pyrenees to take the overall leader's yellow jersey.
And while Pogacar clawed back a few seconds here and there, the defending champion never relinquished the lead all the way to Paris.
Runner-up in 2021, the softly-spoken Vingegaard was the only rider to challenge the Slovenian prodigy in the high mountains.
In 2022, he went one step higher and won the title at altitude, and it proved to be the case again in 2023, but with a Tour of such poise and dominance his claim to be targeting a third straight title must be taken seriously.
"The Tour de France is the greatest race in the world," beamed the 26-year-old.
"There's something so special about it and I can tell you I'll be back again next year to try and win it again."
