Fabio Baldato of Italy won the 147.5km 21st and final stage from Palaiseau to Paris, beating Frenchman Frederic Moncassin in a sprint finish up the Champs Elysees.
Jeroen Blijlevens of the Netherlands, winner of the fifth stage into Besancon, was third.
Baldato, who won the stage to Lannion last year, seized the initiative after the peloton had engulfed a group of four escapees. Moncassin, winner of two stages in the Tour, locked onto his wheel but was unable to overpower him in front of a seething crowd of over 60,000 people -- an estimated 20,000 of whom had travelled from Denmark to cheer Riis' victory.
Riis, 32, ended Miguel Indurain's five-year reign as champion, finishing almost two minutes clear of teammate Jan Ullrich of Germany, while Richard Virenque of France finished third overall -- the first Frenchman on the podium since 1989.
Moncassin, a member of the French Olympic team, sportingly slapped Baldato on the back in congratulation after they crossed the line.
Earlier, three Italians, Andrea Tafi, winner of this year's Paris-Roubaix classic, Flavio Vanzella, who wore the yellow jersey for four days in 1994, Massimo Podenzana, winner of the stage to Villeneuve-Sur-Lot, and Russian Andre Tchmil built up a lead of 48 seconds after the fourth of the eight circuits round Paris.
The four, though, were never going to be able to let the sprinters miss their last day of glory and their brave, but foolhardy, escape ended as they swept up the Champs Elysees for the final time.
The peloton had been in a very merry mood prior to their arrival in Paris with France's Pascal Herve, who won 10,000 Francs (3,000 dollars) for being second over the Aubisque climb on Wednesday, drinking a glass of champagne while riding and Chris Boardman, finishing his first Tour in three attempts, dancing with Australian Neil Stephens side by side on their bikes.
The joy at surviving was a natural reaction by the 129 survivors out of the original 198 starters -- who endured one of the hardest Tour's in recent memory.
The Spaniard, who had been in a class of his own in each of the last five Tours, proved he was only human by suffering two bad days in the Alps and in the Pyrenees to end a modest 11th overall over 14 minutes back.
``I knew this would happen to me one day and I was prepared for it,'' said Indurain, who will try to restore some pride in the Olympics in Atlanta, where he will go for gold in both the road race and the time-trial.
The man who deprived him of a record sixth win in the world's greatest cycle race was one rarely mentioned in the lists of pre-race favourites.
Like Indurain, the leaders of the new generation, starting with Swiss Alex Zuelle and Russian Evgeny Berzin, struggled in atrocious conditions with cold, rain and even snow followed by stifling heat.
And the balding Riis, who is 32 -- the same age as Indurain -- seized his chance to shine after spending years in the shadow of others. He became the oldest Tour winner since Dutchman Joop Zoetemelk, who was 33 when he won it in 1980.
The powerful Dane had already attracted attention by finishing fifth of the 1993 Tour and third last year but until this year, he had to work for his leaders.
He became the boss at last by joining German stable Telekom this season and, with precious help from his team mates, he stamped his authority on the race.
With two brilliant stage wins, one in the Alps and one in the Pyrenees, he dominated the mountain stages and in the others, he controlled his pursuers with plenty of cool.
Thousands of Danish fans waving red and white banners were waiting for him in the French capital and met his triumph with loud applause as he came in safely within the pack, letting Italian Fabio Baldato win a mass sprint to take the last stage. ``This is the best day in my career, I'm so happy,'' said Riis after parading on his bike up the Champs-Elysees with a Danish flag. ``There were so many Danes here, it was just unbelievable.''
He then kissed his wife Mette and his two sons, Jesper and Thomas, who were allowed to try on their father's yellow jersey.
Can Riis do it again next year?
Maybe, but he will have to keep and eye on the revelation of this year's Tour, his young German team mate Jan Ullrich, who came second overall one minute and 41 seconds behind his leader in his first Tour.
His superb win in Saturday's penultimate stage, a demanding time-trial over 63.5 kms from Bordeaux to Saint-Emilion, suggested the 22-year-old from Rostock might go for more than just second place in the near future.
Even Indurain was impressed. ``It's quite remarkable when you think that he has been helping Riis all the time,'' said the Spaniard. ``He's still very young and he certainly looks like he could win a Tour, if not several.''
But Ullrich said he needed time. ``The team was so great because Bjarne was in the lead,'' he said. ``To see him do so well boosted our confidence and anyway, he was much stronger than I was in the mountains. He's got plenty of experience. I've still got a lot to learn.''
Third-placed Richard Virenque, who became the first Frenchman to make the podium since Laurent Fignon was second in 1989, will also stand a chance. He proved this year he is more than just a mountain specialist.
Another one to watch will be Spaniard Abraham Olano. He might have done much better than ninth if he had not concentrated on working for his leader, 35-year-old Swiss Tony Rominger, who lost his last chance to win the Tour by ending 10th.
Next year, Virenque and Olano will be 27, the age Indurain was when he won his first Tour.
But according to Riis, the favourite could be Indurain again. ``He was not at his best this year but he's still a great champion and he will come back next year to win it, I'm sure,'' he said.
After years in the shadow of others, the discreet Dane came of age at last on Sunday by clinching the world's greatest cycle race in Paris.
Now he will open one of the 600 bottles in his cellar -- probably a Chateau-Rothschild he had been advised to keep.
When the Tour de France started last month from the Dutch city of Den Bosch, everybody was looking for a young rider who might beat Miguel Indurain and deprive the mighty Spaniard of a record sixth straight win.
But it was a balding 32-year-old regarded as merely a useful team mate who came along and confidently stamped his authority on the race in the way Indurain used to.
Riis was not exactly unknown -- he had finished fifth overall in the 1993 Tour and third last year -- but few listened carefully when he repeatedly said before the race he had never felt so strong.
``Since joining us he has been telling us that his goal was to win the Tour,'' team director Walter Godefroot said. ``He wanted to know if the guys would be strong enough to support him and I told him that if he behaved as a leader they would do their utmost to help him. That's exactly what happened.''
The softly-spoken shy Riis was known for his all-round ability but he had to wait until this season -- his 11th on the professional circuit -- to become his team's leader.
``I realised for the first time that I could win this race when I came fifth in 1993, but to succeed I needed to be a leader,'' he said.
Riis was struggling with Toshiba in 1988 when two-time Tour winner Laurent Fignon of France asked him to join him in the Super-U stable.
``Nobody was interested in him but there were signs, like the way he could ride in climbs or set the pace in front of the pack, which proved he was a great rider,'' Fignon said.
For three years Riis concentrated on helping the Frenchman and had to be pushed to seize opportunities for himself.
``I remember one time in the 1989 Giro when somebody had broken away,'' Fignon said. ``Bjarne could chase him but he wanted to stay with me. I told him: ``Go for it, what are you waiting for?' He went eventually and won the stage.''
Then came the Italian years with Ariostea and Gewiss. In those wealthy well-organised teams Riis slowly matured to become a potential Tour winner.
``I studied the way Indurain won his Tours and I thought of ways of beating him,'' he said.
But he did not get on with Gewiss's Russian rider Evgeny Berzin and was happy to sign for Telekom.
``I feel strong, I think I can win,'' he warned again a few days after this year's Tour set off.
Riis was frustrated when the ninth stage to Sestriere, which should have been the toughest of the Tour, was shortened to 46 km because of awful weather.
But he had decided it was to be his day and attacked in the only difficult section of the truncated stage -- the punishing final climb to the Italian resort.
Nobody could follow. Riis seized the coveted yellow jersey and kept it until the traditional finale on the Champs-Elysees.
He won a memorable stage win in the Pyrenean ski village of Hautacam, and in an exhausting ride to Pamplona in Spain the following day only Swiss Laurent Dufaux, who narrowly beat him to claim the stage, could keep up with him.
``He's incredibly strong,'' said an impressed Dufaux. ``He's so determined. He always wants to remind everybody he's the boss.''
Aware he is not young anymore, Riis has refused to make plans and is looking forward to spending a few days with his wife, Mette, and his two sons, Jesper and Thomas.
On Thursday he will leave for Atlanta. On July 31, after the Olympic road race, he may open another of his expensive wines.
Indurain, a five-times Tour winner, had told reporters on Saturday he had still not made a decision about going to Atlanta.
The 32-year-old Spaniard, bidding for a record sixth win in the world's greatest cycle race ending later on Sunday, had two days of disappointing performances in the mountains and dropped to 11th place overall.
After having animated a few stages and finished close to the top several times, Fabio Baldato was the last great sprinter to win a stage today as he beat Frederic Moncassin, Jeroen Blijlevens, Djamolidin Abdoujaparov and Erik Zabel.
This battle concludes the Tour, with Riis's 22-year-old teammate Jan Ullrich finishing in second place, Zabel the best sprinter, Richard Virenque the best climber in third place and his Festina men atop the team standings.
Just as usual in this last stage, the peloton let the last rider in the standings clear the Tour's last climb in front, making sure he doesn't go home penniless.
And just as usual, the field fastened its pace once it saw the Eiffel Tower. But after short, unsuccessful attacks, four men went clear when the field first passed the finish line on the Champs Elysees, with 50 kilometers left in the stage.
Amazingly, Vanzella, Podenzana, Tafi and Tchmil would stay in front until the last kilometer. After the sprinters' teams (Gan, Telekom, Refin and TVM) brought the field back to them, the sprint opposed the best of them, Zabel, Moncassin, "Abdou," and Blijlevens in a final all-out war. Until those in Atlanta, that is...