"The win one Tour is a dream. To win six is just unbelievable", said the American on Sunday, who returned from a near fatal cancer in 1999 to win the first of an unprecedented series of Tour victories.
"The Tour is my pal," added the Texan after a lap of honour on the Champs Elysees.
The American crossed the line at the back of a split bunch of 147 riders left in the Tour after three weeks and 3,500 km of racing, at the end of the 163-km last stage from Montereau to Paris won by Belgian Tom Boonen.
German Andreas Kloeden was second overall, six minutes and 19 seconds behind the U.S. Postal team leader and Italian Ivan Basso was third, 6:40 adrift.
"The Tour de France is the most beautiful race in the world. For me, for cycling, for my team, for my new sponsor Discovery Channel, I cannot think of not doing another year on the Tour de France," Armstrong told French television.
"We'll see..." he added.
Thanks to his victory in 83 hours 36 minutes and two seconds, Armstrong, who won five individual stages this year, eclipsed former five times Tour winners Eddy Merckx, Bernard Hinault, Jacques Anquetil and Miguel Indurain.
The 2004 Tour was the second fastest in history after last year's at an average speed of 40.553 kph.
Boonen outsprinted the main bunch to snatch his second stage victory this year, but it was not enough for the Belgian to prevent Australian Robbie McEwen from winning the points classification green jersey for the second time.
"It's a real team victory," said Boonen, whose Quick Step team won four stages.
McEwen, who was fourth in the stage behind Frenchman Jean-Patrick Nazon and German Danilo Hondo, won the green jersey in 2002.
"Green is my favourite colour," said the Lotto-Domo
VIRENQUE RETIREMENT?
The King of the Mountains classification went to Frenchman Richard Virenque, who also beat a record by wining the distinctive polka dot jersey for the seventh time.
Asked if he would return for an eighth climber's jersey, he said: "I'm not sure, we'll see."
Russian Vladimir Karpets won the white jersey for the best young rider while the team classification went to Kloeden's and fourth-placed Jan Ullrich's T-Mobile team.
Usually a relaxed ride through the outskirts of Paris to the Champs Elysees, the final stage was a little bit more animated than usual as Italian Filippo Simeoni attacked three times to try and spoil Armstrong's show.
The Domina Vacanze rider and the Texan are involved in a bitter legal battle and Simeoni was out for revenge after Armstrong forced him back into the main bunch after he had tried to attack in Friday's 18th stage.
Simeoni finally calmed down and Armstrong, surrounded by his U.S. Postal team-mates sporting golden helmets, took the time to sip champagne in the bunch before letting sprinters battle it out for the stage honours on the Champs Elysees.
Before climbing on the podium for the sixth time, Armstrong was greeted by his friends, actors Will Smith and Robin Williams and received a phone call from another famous Texan, president George W. Bush.
"You're awesome," Bush told Armstrong in a phone call from his ranch near Crawford, Texas, according to the White House.
Bush, who cycles for exercise, had watched the race finish on television before calling Armstrong at about 1600 GMT (5 p.m. British time).