The rumors were true: Stephen Colbert will replace David Letterman as host of The Late Show when Letterman retires next year, CBS announced today. The Colbert Report host has a five-year deal with the network, but it's not clear when he'll start, as Letterman has yet to chart the timing of his final 2015 shows. Also up in the air for now: the show's location and producers. "Simply being a guest on David Letterman’s show has been a highlight of my career," Colbert says in the statement. "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."