The former cyclist said his attempts to destroy team masseuse Emma O'Reilly's reputation were "inexcusable and embarrassing".
Armstrong has walked to the border of truth many times before but has yet to cross it; now he smells a chance at a reduced ban from sport.
Sir Bradley Wiggins said it was "emotional" watching Lance Armstrong admit to using performance-enhancing drugs.
The Sunday Times was forced to settle a claim with Lance Armstrong in 2006 and agreed to pay him £300,000, the newspaper reported (£).
But after his sensational confession the paper launched a High Court bid to return the money, plus £720,000 in costs, and have now reached a confidential settlement, the newspaper said today.
It said Walsh and English had "reached a mutually acceptable final resolution to all claims against Lance Armstrong related to the 2012 High Court proceedings and are entirely happy with the agreed settlement, the terms of the which remain confidential.
Disgraced cyclist Lance Armstrong has reached an agreed settlement with The Sunday Times, which had accused him of deceit and sued him for more than £1 million, the newspaper (£) is reporting.
In 2004, Armstrong had sued the newspaper for libel after it published an article suggesting he might have used performance-enhancing substances.
He then sought damages from the newspaper's chief sports writer David Walsh and Alan English, who was deputy sports editor.
Tour de France leader Chris Froome admitted his frustration over questions about doping a day after his impressive stage win.
The British cyclist won on Mont Ventoux - one of the most feared climbs in cycling - but his performance was compared to those of Lance Armstrong, who was stripped of seven Tour titles for doping.
On the doping questions, Froome said: "I just think it's quite sad that we're sitting here the day after the biggest victory of my life, a historic win, talking about doping.
"My team-mates and I have been away from home for months training together and working our arses off to get here, and here I am accused of being a cheat and a liar."
He added: "Lance cheated. I'm not cheating. End of story."
The 100th edition of the Tour de France has started on the French island of Corsica.
Disgraced cyclist Lance Armstrong has sought to clarify recent comments made in French newspaper Le Monde about winning the Tour de France.
He was quoted as saying it would be impossible to win the famous race without doping, however he took to Twitter to say
For the record, there is a significant difference between WAS and IS. Past and present tense.
Read: Armstrong: 'Impossible' to win Tour without doping
The 100th Tour De France will begin today with 212km stage one from Porto-Vecchio to Bastia in Corsica.
Last year's runner-up to Sir Bradley Wiggins, Chris Froome, will lead Team Sky and is favourite to become the second British winner.
Wiggins is unable to compete this year due to illness and injury.
He said: "It is very sad that Lance Armstrong has decided to make this statement on the 100th anniversary of the Tour de France. However, I can tell him categorically that he is wrong. His comments do absolutely nothing to help cycling.
"The culture within cycling has changed since the Armstrong era and it is now possible to race and win clean.
"Riders and teams owners have been forthright in saying that it is possible to win clean – and I agree with them.
“Cycling today has the most sophisticated anti-doping infrastructure in sport. Measures such as the introduction of the blood passport, the whereabouts system and the ‘no-needle’ policy are the backbone of our relentless fight against doping."
Disgraced cyclist Lance Armstrong, who cheated his way to win seven Tour de France titles, said it would have been impossible to win the famous race without doping.
"My name was taken out of the palmares (list of achievements) but the Tour was held between 1999 and 2005 wasn't it?
"There must be a winner then. Who is he? Nobody came forward to claim my jerseys."
Bernard Hinault, who won the Tour five times, reacted by telling TV channel BFM: "He must not know what it was like to ride without doping."