Stephen Colbert will be the new host of "The Late Show" (Twitter/@TheWrap)

Though just one of many names thrown around as a potential replacement, Colbert has gained a strong reputation as a correspondent on “The Daily Show” and then as the host of his own Comedy Central show, “The Colbert Report.”

“Simply being a guest on David Letterman’s show has been a highlight of my career,” Colbert said. “I never dreamed that I would follow in his footsteps, though everyone in late night follows Dave’s lead. I’m thrilled and grateful that CBS chose me. Now, if you’ll excuse me, I have to go grind a gap in my front teeth.”

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Jon Stewart, one of the other frontrunners for the “Late Show” gig, voiced his support for Colbert in an interview with Vulture.

“He’s got some skill sets that are really applicable, interviewing-wise, but also he’s a really, really good actor and also an excellent improvisational comedian. He’s also got great writing skills. He’s got a lot of the different capacities,” Stewart said.

The exact details of the show haven’t been decided yet, including producers, writers and location, but according to EW, Colbert will be bringing over his staff from “The Colbert Report.”

Colbert will begin his new hosting gig when Letterman steps down sometime next year.