The confession followed a USADA investigation which implicated Armstrong as a central figure in what it called "the most sophisticated, professionalised and successful doping programme that sport has ever seen".
He was stripped of all results from August 1, 1998 and banned from sport for life.
McQuaid said: "Lance Armstrong's decision finally to confront his past is an important step forward on the long road to repairing the damage that has been caused to cycling.
"Lance Armstrong has confirmed there was no collusion or conspiracy between the UCI and Lance Armstrong. There were no positive tests which were covered up and he has confirmed that the donations made to the UCI were to assist in the fight against doping."
However, former rivals, friends and sports figures were united in their condemnation of Armstrong.
Two-time Tour de France stage winner Robbie McEwen of Australia said he could never forgive Armstrong, adding he "deceived everybody on the planet, us included."
WADA president John Fahey said that Armstrong's claim that he wasn't cheating when he took part in doping through his seven Tour de France wins "gives him no credibility."