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It’s official: Stephen Colbert will replace David Letterman as CBS’ Late Show host.

The broadcast network has tapped the 49-year-old Comedy Central host to take over the late-night franchise.

CBS has made a five-year deal with Colbert, which was announced Thursday by CBS Corp. CEO Les Moonves and CBS Entertainment chairman Nina Tassler.

“Stephen Colbert is one of the most inventive and respected forces on television,” Moonves said. “David Letterman’s legacy and accomplishments are an incredible source of pride for all of us here, and today’s announcement speaks to our commitment of upholding what he established for CBS in late night.”

Letterman, the longest-serving late-night TV host, announced his retirement on April 3. Colbert’s premiere date will be announced after Letterman determines a timetable for his final broadcast in 2015.“Stephen is a multi-talented and respected host, writer, producer, satirist and comedian who blazes a trail of thought-provoking conversation, humor and innovation with everything he touches,” Tassler added. ”He is a presence on every stage, with interests and notable accomplishments across a wide spectrum of entertainment, politics, publishing and music. We welcome Stephen to CBS with great pride and excitement, and look forward to introducing him to our network television viewers in late night.”

“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.”

Sources say Colbert informed his Colbert Report staff a couple hours ago and that he told his team they’re all going to work on his CBS show.

Comedy Central released this statement: “Comedy Central is proud that the incredibly talented Stephen Colbert has been part of our family for nearly two decades. We look forward to the next eight months of the ground-breaking Colbert Report and wish Stephen the very best.”

Colbert is expected to shed his ultra-conservative Colbert Report character for Late Show, which leads to perhaps the biggest question mark surrounding his hiring. Though he’s been going through the broad motions of being a late-night host since 2005, he hasn’t been “himself” on the air — so what does that look and feel like, exactly?

Colbert’s fellow Comedy Central host Jon Stewart assured Vulture: “He’s got a lot more he can show. 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. Being able to expand upon [those] would be exciting.”

The announcement brings a surprisingly quick and efficient close to the speculation about who will replace Letterman, especially when compared to some of the agonized drama that’s typified NBC’s late-night upheavals over the years. Some maintained that CBS should break up the white-male late-night club by hiring a woman or a person of color to fill the Late Show post. Yet Colbert was quickly the odds-on favorite for the post — quite literally, as an online sportsbook gave the Comedy Central 3:1 odds at taking over the coveted gig.

UPDATE: Letterman released this statement: “Stephen has always been a real friend to me. I’m very excited for him, and I’m flattered that CBS chose him. I also happen to know they wanted another guy with glasses.”