"This is surreal for me. I'm not gonna lie," Noah said, launching into the show-opening monologue Monday night.
"Growing up in the dusty streets of South Africa, I never dreamed that I would one day have two things really: an indoor toilet and a job as host of the Daily Show. And now I have both, and I'm quite comfortable with one of them."
Until being named to take over as the show's host, the 31-year-old was not well known in the United States. He has done stand-up comedy around the world but on "The Daily Show" he appeared as a contributor just a few times.
Some of Stewart's people have remained on the set, providing a degree of continuity for the four-times-a-week show.
- Hard act to follow -
But the 52-year-old Stewart, who retired August 7 after a 16-year run on Comedy Central network, is a hard act to follow.
He turned the show into a unique cocktail of politics, journalism and entertainment that skewered politicians, the world in general and sensationalist cable news coverage in particular.
He was loved by liberals as a voice of reason and distrusted by conservatives for his left-of-center perspective.
He became such a towering figure in the competitive world of late-night American TV comics that he landed President Barack Obama as a guest no fewer than seven times. He won more than 20 Emmy awards.
"He was often our voice, our refuge. And in many ways our political dad," said Noah, in one of his many praise-filled acknowledgements of his predecessor.
"And it's weird, because dad has left. And now, it feels that the family has a new stepdad. And he's black, which is not ideal."
Throughout the show, Noah was as sharp and funny as Stewart, although he didn't break much new ground.
The studio audience seemed to love him.
"He's more of a charmer," said Andrew Wynner as he exited the show. "He has a lot of charisma."
But he added: "It was more a getting-to-know-you kind of show."
"He's the best I could have imagined to replace Jon Stewart," said Sabrina Illiano, a Columbia University student in the audience.
Noah, born and raised in apartheid-era South Africa of a mixed-race marriage, says he will try to give "The Daily Show" his own unique flavor.
Stewart told him to, he says.
- 'Make your show' -
"He specifically said: 'Make your show. Make your best version of it,'" Noah told the New York Times ahead of Monday's show.
"Jon's suggestions were very simple and yet very difficult to decipher. He's like a Jewish Yoda. He said to me: 'Make the best show that you feel needs to be made. And trust your discomfort.'"
Noah said he will try to broaden the horizons of the largely US-angled show, although Stewart did love to talk about foreign policy.
"I think, naturally, the show will be a representation of my interests, and the interests in the room," he said.
"We all live in America. But as America is increasingly learning, if a butterfly flaps its wings on the Chinese stock exchange, there's a good chance it affects America," he told the Times.
- Holy hashtaggery -
Noah has been dogged by criticism of Twitter posts he has made that some found offensive to women and Jews. He has had an account since 2009 and boasts more than 2.5 million followers.
Take this one from 2011: "Oh yeah the weekend. People are gonna get drunk & think that I’m sexy! - fat chicks everywhere."
Another, from 2009: "Almost bumped a Jewish kid crossing the road. He didn't look b4 crossing but I still would have felt so bad in my german car!"
Noah says those tweets are from years ago and he has since changed.
"If you look back three years and you're not disappointed in who you were then, you're not progressing," he said this month in an interview with Entertainment Weekly.
People jump onto Twitter hashtag trends -- like those who bemoaned his tweets -- without really understanding what's going on, Noah said.
These days people live in a "world of faux outrage. It's hashtag this, hashtag that."
"Then you have an artificial inflation of what the problem is. All of the sudden you get all of these big scandals, but they're not big, because everyone is on the periphery of the argument," Noah added.