CBS announced Stephen Colbert will replace David Letterman as its late-night TV host when Letterman retires in 2015.

“Stephen Colbert is one of the most inventive and respected forces on television,” CBS Chairman and CEO Les Moonves said in a statement Thursday. “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.”

Colbert, 49, signed a five-year deal with CBS. In a statement, Colbert: “Simply being a guest on David Letterman’s show has been a highlight of my career. 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.”

And in case you were wondering, Colbert won’t be “Stephen Colbert” but himself. We’ll all find out who that is in the years to come.  “I won’t be doing the new show in character, so we’ll all get to find out how much of him was me,” he said. “I’m looking forward to it.”

The timing of the transition is still to be determined. Mostly by Letterman and his Late Show/Worldwide Pants people. Updated: Moonves said the new Late Show will be a CBS production and NOT Worldwide Pants.

But that also means it’ll still be the Late Show and still be broadcast in NYC.

It also means Comedy Central will have a half-hour to fill between The Daily Show with Jon Stewart and @midnight at 11:30 p.m. Eastern/Pacific Mondays-Thursdays, once Colbert signs off there. Which should be end of the calendar year.

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

Other reactions:

Letterman’s first official statement read, “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.” You can be sure to hear more out of Dave on this topic on tonight’s program.

Ferguson @CraigyFerg: “Congratulations to the hugely talented and fragrant and lovely @StephenAtHome on the new gig. Welcome to the CBS funhouse.”

Jimmy Kimmel @Jimmy Kimmel: “Congratulations to @StephenAtHome #StephenColbert – a finer or funnier man I do not know.”

Jimmy Fallon @Jimmy Fallon, Colbert’s “BFF” in late-night: “I’d like to welcome the great @StephenAtHome to network late night and also congratulate him on his new name: Jimmy Colbert.”

UPDATED with Les Moonves on CBS Radio today, saying Colbert “fits with who we are” and was the singular choice — “Very obvious that Stephen was the best for this position.” He and his wife are big fans. And he confirms that Colbert will end his Comedy Central show and facade at the end of 2014, to re-emerge as the real Stephen Colbert on CBS sometime in 2015. Moonves said about “a dozen” out of hundreds of names were actually serious candidates to replace Letterman. He also says in this interview that Worldwide Pants will not be producing Colbert’s “Late Show,” and that the location may not be the Ed Sullivan Theatre, either! It’s all up for grabs, except for the new host.

So what happens with the late-late slot at 12:35 a.m. Eastern/Pacific, now? Time will tell…

Related: My other observations on that front.