Hamilton said he saw Armstrong take performance-enhancing drugs, EPO and testosterone and also saw him receive a banned blood transfusion in 2000.
"I feel bad that I had to go here and do this," Hamilton said in his first public admission of doping throughout his career. "But I think at end of the day, like I said, long-term, the sport's going to be better for it."
In the interview, Hamilton revealed other observations about the US Postal team operation:
-Team leaders, including doctors and managers, encouraged and supervised doping;
-Doping was going on inside the US Postal team even before Armstrong joined in 1998;
-Performance-enhancing drugs, including EPO and human growth hormone, were handed out to cyclists in white lunch bags;
-Team members were met at the airport, driven to hotels, told to lie down and give blood that could be transfused back into their bodies at a later date.
Armstrong long has denied doping and has never tested positive.
On Sunday, his attorney, Mark Fabiani, released a statement deriding the CBS report.
"We have already responded in great detail at www.facts4lance.com," Fabiani said. "Throughout this entire process, CBS has demonstrated a serious lack of journalistic fairness and has elevated sensationalism over responsibility. CBS chose to rely on dubious sources while completely ignoring Lance's nearly 500 clean tests and the hundreds of former teammates and competitors who would have spoken about his work ethic and talent."
The "60 Minutes" report used unidentified sources to report that another Armstrong teammate and close friend, George Hincapie, testified to the grand jury investigating doping within cycling that he and Armstrong supplied each other with EPO and discussed having used testosterone to prepare for races.
Armstrong posted a statement in support of Hincapie on the website: "We are confident that the statements attributed to Hincapie are inaccurate and that the reports of his testimony are unreliable."
Hincapie released a statement on Friday, through his lawyer, saying he did not speak with "60 Minutes" and didn't know where the show got its information.
Hamilton, meanwhile, described a systematic doping programme run by Armstrong's US Postal team. He said he offered the same testimony to the Los Angeles-based grand jury.
Federal prosecutors are investigating what essentially would have been a drug distribution network that was formed to keep Armstrong's teams running at the head of the pack.
The "60 Minutes" revelations, combined with recent requests from federal authorities for evidence in France, have fed a sense of growing trouble for the world's most famous cyclist, an international star and a cancer survivor who has raised millions of dollars to fight the disease.
In his interview, Hamilton said he saw Armstrong use the blood-boosting drug EPO during the 1999 Tour de France and in preparation for the 2000 and 2001 tours.
Armstrong won the world's most-revered race each year from 1999-2005.
But the case federal authorities are trying to compile won't be decided solely on whether Armstrong doped. It has more to do with a doping programme allegedly run by the cyclist and his team - a programme that could lead to fraud and conspiracy charges.
"He obviously was the biggest rider in the team and he helped to call the shots," Hamilton said. "He doped himself, you know, like everybody else, but he was just being part of the culture of the sport. ... He was the leader of the team and he expected for going in, for example the '99 Tour, (that) we were going to do everything possible to help Lance win. We had one objective, that's it."
The Associated Press reported last month that federal investigators asked French authorities to turn over evidence, including Armstrong's urine samples from 1999, the same year Hamilton said he saw Armstrong use the EPO during the Tour.
Armstrong's 1999 samples came under scrutiny in 2005 when the French sports daily L'Equipe reported that six of the samples had, in fact, tested positive for EPO when they were retested in 2004. An investigation by the International Cycling Union followed and concluded that the samples were mishandled and couldn't be used to prove anything.
But the samples still exist and are part of the cache of evidence authorities are seeking.
Those samples, along with bank and phone records and witness testimony about drug use, could be used to paint a picture of a doping programme allegedly run by Armstrong and his US Postal team.
Also in the "60 Minutes" report, Hamilton said Armstrong told him he had tested positive at the 2001 Tour de Suisse - a warm-up race for the Tour de France - but that he wasn't worried about it.
"He was so relaxed about it and he kind of just said it off the cuff and kind of laughed it off," Hamilton said. "It helped me sort of stay relaxed because, obviously, if he had a positive test, the ... team's going to lose the sponsorship, I'm going to lose my job. Not only am I going to lose my job but, you know, 50 to 60 other people are going to lose their jobs. ... There were a lot of consequences to a positive test."
Hamilton said Armstrong made a deal with the UCI, and they "figured out a way for it to go away."
The Tour de Suisse allegations are similar to those made by Floyd Landis, who had his 2006 Tour de France title stripped for doping. After years of denying he cheated, Landis came out last year acknowledging he used PEDs and alleged Armstrong did, as well.
The "60 Minutes" report referenced a letter provided by Armstrong's attorney that says UCI claims none of the positive samples belonged to Armstrong.
Also in the interview, Hamilton said Armstrong and Italian trainer Michele Ferrari talked about PEDs and when and how to take them.
"He taught Lance how to train properly," Hamilton said. "Obviously, in cycling, there's more than just training and resting and eating correctly. There's one more element - the doping part. And he gave him, you know, a doping schedule."
Ferrari, who has been banned for life by the Italian Cycling Federation, is being investigated in Italy. Armstrong said he has severed formal ties with Ferrari but has acknowledged meeting him nonprofessionally since then. Last month, the AP reported the two had met as recently as last year, before the Tour de France, which was Armstrong's last Tour before he retired for the second time.
Armstrong's new website attacked Hamilton, who has been banned twice for doping despite his long insistence that he never cheated. Hamilton now admits he did use PEDs and has given his 2004 Olympic gold medal to the U.S. Anti-Doping Agency.
"Tyler Hamilton is a confessed liar in search of a book deal - and he managed to dupe '60 Minutes,' the 'CBS Evening News,' and new anchor Scott Pelley," the website said. "Most people, though, will see this for exactly what it is: More washed-up cyclists talking trash for cash."