The 25-year-old won the final day's time-trial with defending champion Jonas Vingegaard coming second at 1 minute 03 seconds on the day to seal second overall ahead of Remco Evenepoel, third on the day and also third overall.
Victory also gave Pogacar the first Giro d'Italia-Tour de France double since Marco Pantani in 1998.
"It was an amazing journey. What a battle with Jonas and Remco. So much happened," said the champion who finished 6mins 17secs ahead of Vingegaard in the final standings. Evenepoel was 9mins 18secs off the pace.
"We are living in the golden age of cycling. The rivalry with Remco (Evenepoel), Jonas (Vingegaard), Primoz (Roglic) is just incredible. We have to take advantage of this moment."
Astonishingly Pogacar won six stages on this edition of the Tour, just as he did when winning the Giro earlier in the season.
"To achieve the double is incredible," added Pogacar who had been runner-up to Vingegaard for the last two years.
'Next level'
"When I won the Giro, some people said that it would serve as a safety net for me if I didn't win the Tour. Winning the Tour still represents the level above and winning the two is the next level."
The world's greatest bike race, broadcast across the globe, featured a novelty finale on the French Riviera because of the Olympic Games in Paris.
Instead of the last day race around the Champs-Elysees the Tour avoided the Olympic Games sites altogether.
With five stage wins already under his belt, Pogacar stormed out of his adopted hometown of Monaco and up the coast to Nice where he leapt into the arms of his teammates on the celebrated Promenade des Anglais.
Pogacar took the overall lead on a downhill on day four as the race arrived in France from Italy via the Alps.
By the time the race returned to the Alps, Pogacar was three minutes clear and Vingegaard was starting to flag with the Dane still not fully recovered from a major crash in March.
After winning stage 19 on Friday, Pogacar knew he had won and Vingegaard switched his attention to finishing second.
Vingegaard crashed heavily earlier this year and was praised for even making it to the start line, but ahead of Sunday's time-trial he expressed a desire to win another stage.
"Under normal circumstances I would have been disappointed. This is such a wonderful race, the yellow jersey is the most beautiful of all. I'll be back to try for a third one next year," said the 27-year-old.
Although he started well, as has often been the case in this Tour, he was a distant second best.
He did however beat pre-race favourite Evenepoel, who cried at the finish line.
There are many prizes on offer on the Tour with Pogacar's yellow jersey for overall race leader being the chief amongst them.
'On another planet'
Evenepoel may not have won the final day time-trial but he captured the first time-trial in week two.
He also came third in the overall standings and won the white jersey for best young rider.
"Tadej is on another planet, I have a gap to bridge between me, Tadej and Jonas, but this was a good Tour, a good test for me," said the 24-year-old Belgian.
Other stars emerged along the way as Eritrean rider Biniam Girmay won three stages, the sprint points green jersey and national hero status in his homeland.
Riding a green bike and also decked out from head to toe in the colour, Girmay was seen off by a clutch of his countrymen in Monaco.
"It's astonishing," the Eritrean said. "The feelings, the emotions, I want to share them with the people from my country."
Olympic champion Richard Carapaz won a stage, took the yellow jersey for a day and came close to other victories. He raced on Saturday in the polka dot best climber's jersey.
Mark Cavendish also took the headlines, claiming a record 35th stage win and was given a special podium presentation for his career achievement.
Greeted by his family in Nice there were no tears from the "Manx Missile".
"There are a hundred and seventy odd cyclists in this race, and most of them finish a Tour winning nothing," Cavendish said after his podium award.
When asked if this was his last Tour he replied: "Yes 100 percent."
