"On Monday, Comedy Central will announce that Mr. Noah has been chosen as the new host of The Daily Show, succeeding Mr. Stewart after he steps down later this year," the newspaper said.
Noah, who was born in South Africa in 1984, was one of the newest correspondents on the wildly popular show. After joining the show in December, Noah was one of the comedians speculated about as a possible successor when Stewart, 52, announced in February that he was leaving the show.
Other possible contenders included Canadian-American comedian Samantha Bee, Last Week Tonight host John Oliver and Daily Show correspondent Jessica Williams.
"You don’t believe it for the first few hours," Noah told the New York Times from Dubai where he is currently on a sold-out comedy tour. "You need a stiff drink, and then unfortunately you’re in a place where you can’t really get alcohol."
Who is Trevor Noah?
While Noah isn't a household name, the established comedian and writer has sold more DVDs than any other standup on the African continent, his website boasts. He has also hosted a number of television programs in his native South Africa, and has appeared on high profile American programs such as The Tonight Show with Jay Leno and the Late Show with David Letterman.
Noah also has an established following on social media. Two million people follow him on Twitter, where he has tweeted observant one-liners on international politics, popular culture and the murder trial of Olympian Oscar Pistorius.
Canadian fans of The Daily Show can get a sneak peak at Noah's comedy when he brings his Lost in Translation comedy tour here in November. Dates and cities for the tour haven't been announced yet.
As for Stewart, the long time host is expected to give up his seat behind The Daily Show desk later this year, but Comedy Central has yet to announce an exact date when he'll pass the torch to Noah.