Armstrong awoke early Wednesday morning in Adelaide, Australia, hours before the second stage of the Tour Down Under, to watch Obama's inauguration.
The seven-time Tour de France champion, making a return to competitive cycling after three years in retirement, said he had often been asked what he thought of the new president.
"I can tell you that in my three or four encounters with him, meeting with him, he's been delightful, he's been smart, he's been present and he's been committed," Armstrong said.
Armstrong, a testicular cancer survivor, felt Obama identified with his campaign to raise awareness of the disease.
"You can always tell when someone cares about something that you're talking about," he said.
"You know that he lost his mother to cancer, that two days before the election he lost his grandmother to the disease. These are all issues that I care about and we as a constituency care about.
"For the population in general and even for the entire world, we see the first ever African-American president of the United States which is a monumental moment, a monumental achievement. He brings a ton of hope and optimism not just to the U.S. but to everybody all over the world, for our standing around the world and our situation at home."
Armstrong also expressed his concern and best wishes for Senator Ted Kennedy, who suffered a seizure during the inaugural luncheon and is recovering in a hospital.
"Our thoughts and prayers go out to Senator Ted Kennedy," he said. "I spent a lot of time with Senator Kennedy before he was diagnosed (with a brain tumor last year).
"I was honored enough to go testify to a Senate subcommittee and talk about his new piece of legislation that he co-authored...
"It's a huge piece of legislation and if we get this passed it will totally modernize our approach to this disease. And just after that, ironically enough, he was diagnosed with the brain tumor and has been fighting it ever since.
"A lot of people thought he wouldn't be there that long but he's committed to staying in the Senate as long as he can and passing this legislation."