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"No memories of Stewart and his storied reign have been usurped or replaced," wrote The Hollywood Reporter, "Nor, however, have they been sullied."
Daniel Feinberg added: "The best and most honest thing you can say about Monday's premiere is: 'He didn't break it.' He also didn't try to."
Noah's opening monologue kicked off with a joke about growing up on the dusty streets of South Africa, where his only two dreams were hosting The Daily Show and having an indoor toilet.
"Now I have both. And I'm quite comfortable with one of them," said Noah.
Paying tribute to Stewart he said: "He was often our voice, our refuge and in many ways our political dad," before joking, "Now it feels like the family has a new stepdad. And he's black. Which is not ideal."
Deadline's Jeremy Gerard was not convinced by all of Noah's punchlines though.
"A joke about Whitney Houston was DOA, as was a tired play on Aids versus aides, and still the smile never left Noah's face even as the words hobbled out and died... Those teeth need more bite," he said.
But Gawker suggested Stewart fans should stay happy, commenting: "If you liked that Daily Show, this one has some very good news for you: it's basically the same!"
The website said many of Stewart's writing staff had stayed to help "bridge the gap".
"Noah opened with some Pope jokes that sounded like Jon Stewart bits delivered by an extremely handsome man with an accent," Jordan Sargent wrote, concluding, "it could have been a lot worse".
The Guardian's Brian Moylan had little time for Noah's "toothless and unironic interview" with his first guest, actor and comedian Kevin Hart.
"His questions for Hart were such softballs that they may as well have been made out of cotton candy, inflated with helium, and let loose on a spring breeze," said Moylan.
But he added: "Noah had an average first night, neither killing it nor completely embarrassing himself."
This week's guests are Whitney Wolfe, the CEO of dating site Bumble and co-founder of Tinder, the governor of New Jersey, Chris Christie and musician Ryan Adams - who last week released an album of cover versions based on Taylor Swift's 1989 album.
Monday night's debut episode will air in the UK on Tuesday night, on Comedy Central at 23:00 BST.
Viewers in South Africa will be able to watch the show on pay TV service DStv at 21:00 CAT on Comedy Central from Tuesdays to Fridays, with full catch-up episodes available online at www.comedycentralafrica.com from 30 September. - BBC