The decision, supported by Tour organisers, was widely expected given that so many riders finishing behind Armstrong, who was stripped of his titles and banned from the sport for life on Monday, have also been associated with doping offences.
The sport's governing body also called on the American and other disgraced riders to return prize money they had received and said it would set up a "fully independent external commission" to investigate allegations made against it over the Armstrong affair.
Armstrong was formally stripped of his seven titles on Monday when the UCI ratified the United States Anti-Doping Agency's decision to ban the 41-year-old Texan for life and nullify his results from August 1998 onward.
"The management committee decided not to award victories to any other rider or upgrade other placings in any of the affected events," the UCI said following a meeting at a Geneva hotel.
"The committee also called on Armstrong and all other affected riders to return the prize money they had received," the statement added.
Germany's Jan Ullrich finished runner-up to Armstrong three times in the Tour de France but said two months ago he was indifferent as to whether he was handed the titles.
"I've ended my career and I have always said that I'm proud of my second places," Ullrich, second in 2000, 2001 and 2003, said in August. "It doesn't really bother me that much."
Ullrich, Tour champion in 1997, was himself found guilty of doping by the Court of Arbitration for Sport in February, in relation to the Operation Puerto blood-doping scandal that engulfed cycling six years ago.
CAS annulled his results from 2005 until his retirement two years later.
The other riders to finish second to Armstrong were Alex Zuelle of Switzerland (1999), Joseba Beloki of Spain (2002), German Andreas Kloeden (2004) and Italian Ivan Basso (2005).
Zuelle was part of the Festina team thrown out of the 1998 Tour de France after team manager Bruno Roussel confessed the existence of "an organised doping system."
Basso was banned for two years in 2007 for his involvement in Spain's Operation Puerto scandal.
In its statement, the UCI said it "acknowledged that a cloud of suspicion would remain hanging over this dark period - but that while this might appear harsh for those who rode clean, they would understand there was little honour to be gained in reallocating places."
It added that part of the new commission's remit would be to find ways to ensure anyone caught doping would no longer be able to take part in the sport, even as a non-rider in a team.
The UCI will announce on November 5 which independent sports body would nominate the members of the commission, with the appointments to follow as soon as possible. It wanted recommendations published by June 1 next year.
The UCI also announced it was suspending legal action against journalist Paul Kimmage pending the findings of the commission.
Former professional rider Kimmage had alleged the UCI covered up a suspicious Armstrong test, something the governing body denies.
USADA published a report into Armstrong on October 10 which said he had been involved in the "most sophisticated, professionalized and successful doping program that sport has ever seen".
Armstrong, who has always denied doping, had previously declined to contest the charges, prompting USADA to propose his punishment pending confirmation from the UCI which came on Monday.
Former Armstrong team mates at his US Postal and Discovery Channel outfits, where he won his Tour titles, testified against him and themselves and were given reduced bans by the American authorities.
"UCI is determined to turn around this painful episode in the history of our sport. We will take whatever actions are deemed necessary by the independent commission and we will put cycling back on track," said UCI president Pat McQuaid.
"Today, cycling is a completely different sport from what it was in the period 1998-2005. Riders are now subject to the most innovative and effective anti-doping procedures and regulations in sport.
"Nevertheless, we have listened to the world's reaction to the Lance Armstrong affair and have taken these additional decisive steps in response to the grave concerns raised."