The disgraced Texan cyclist made the confession in an interview with US chat show host Oprah Winfrey broadcast on Thursday.
"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 and to restoring confidence in the sport," UCI president Pat McQuaid said.
The Swiss-based International Cycling Union has been accused of colluding with the cyclist to cover-up positive tests and come under pressure to reveal how he was able to avoid detection for so long.
McQuaid noted that Armstrong did not mention any "collusion or conspiracy" but said it was "disturbing to watch him describe a litany of offences" as he cheated his way to seven Tour de France victories and became the sport's most Famous figure.
The Irishman acknowledged that Armstrong's assertion that modern cycling was a different sport from when he was in his heyday, pointing to efforts to clean up the sport, including by introducing biological passports.
He also said the federation welcomed his desire to participate in a "truth and reconciliation process".
The UCI has set up an independent commission to look at its own role in the scandal but has so far refused a partial or full amnesty for cyclists who doped in the past.