The comedian said it had “been an absolute privilege” to have been at the helm of the satirical show since 1999.
Jon Stewart will leave the show later this year.
“This show doesn’t deserve an even slightly restless host and neither do you,” he told his audience on February 10.
Comedy Central president Michele Ganeless paid tribute, saying: “His comedic brilliance is second to none.”
Jon Stewart’s show has often been cited as a leading news source for young people, with an average audience of one million viewers.
His targets – and his guests – have been politicians and public figures, addressed in tones that are often indignant, or teasing.
The Daily Show has also been a launch pad for several well-known comic performers, including Steve Carell and John Oliver, as well as Stephen Colbert.
“I’m going to miss being on television every day,” Jon Stewart said.
“I’m going to miss coming here every day. I love the people here. They’re creative and collaborative and kind.
“It’s been the honor of my professional life, and I thank you for watching it, for hate-watching it, whatever reason you are tuning in for.”
Jon Stewart said he was not sure exactly when he would leave, or what he would do next.
In 2013, the comdien took time out to direct a film, Rosewater, about an Iranian-born journalist who was imprisoned and accused of spying.
“I don’t have any specific plans,” he said.
“Got a lot of ideas, got a lot of things in my head. I’m going to have dinner on a school night with my family, who I have heard from multiple sources are lovely people.”
Comedy Central has not said who will replace Jon Stewart.
His departure comes after the network lost Stephen Colbert, another major comedy figure, who left to take over David Letterman’s late night show on CBS.
In a statement, Michele Ganeless said: “Through his unique voice and vision, The Daily Show has become a cultural touchstone for millions of fans and an unparalleled platform for political comedy that will endure for years to come.
“Jon will remain at the helm of The Daily Show until later this year. He is a comic genius, generous with his time and talent, and will always be a part of the Comedy Central family.”
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