"It's something that I never expected, and I found myself thinking throughout the time, everything we've gone through — the Trump presidency, the pandemic, just the journey, the more pandemic.
"And I realised that after these seven years, my time is up. But in the most beautiful way, honestly."
Noah added, "I've loved hosting the show. It's been one of my greatest challenges. It's been one of my greatest joys. I've loved trying to figure out how to make people laugh even when the stories are particularly s***ty on the worst days. We've laughed together, we've cried together. But after seven years, I feel like it's time."
The South African star paid tribute to show bosses for taking a chance on a "random comedian" who was unfamiliar to US audiences.
He added: "I'm really grateful to a network who believed in this random comedian nobody knew on this side of the world.
"I never dreamed that I would be here. I sort of felt like Charlie and the Chocolate Factory. I came in for a tour of what the previous show was, and then the next thing I knew, I was handed the keys. I couldn't have done it without [the audience], and I wouldn't have wanted to do it without you."
According to Variety, Trevor told the audience at the taping of Thursday's show he was planning to focus on his stand-up comedy work when he leaves the show.
The network confirmed there is not yet a date in place for him to leave.
A spokesperson said: "We are grateful to Trevor for our amazing partnership over the past seven years. With no timetable for his departure, we're working together on next steps.
"As we look ahead, we're excited for the next chapter in the 25+ year history of The Daily Show as it continues to redefine culture through sharp and hilarious social commentary, helping audiences make sense of the world around them."
The Daily Show premiered in 1996 with Craig Kilborn at the helm, before Jon Stewart took over from 1999 to 2015, when he handed over to Trevor.
