Colbert, 49, who has presented the award-winning "The Colbert Report" satirical, fake news show since 2005, paid tribute to Letterman as a model late-night host.
"Simply being a guest on David Letterman's show has been a highlight of my career," he 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," he said, referring to Letterman's gap-toothed smile.
- 'Another guy with glasses' -
Letterman said: "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," he quipped.
Letterman, 66, a pillar of American late-night TV talk shows, announced last week that he will leave his "Late Show" studio at CBS next year after a 22-year run.
Colbert -- who got into hot water recently over offensive language about Asian Americans -- has agreed to a five-year deal with CBS, starting after Letterman stands down.
"Stephen Colbert is one of the most inventive and respected forces on television," said CBS boss Leslie Moonves.
Before launching his eponymous show, Colbert spent eight years as a correspondent on Comedy Central's "The Daily Show" with Jon Stewart, which has won 19 Primetime Emmy Awards.
On "The Colbert Report," which has won four Primetime Emmys, Colbert plays a parody of an ultra-conservative talkshow host, although he himself is widely perceived as liberal.
"I won't be doing the new show in character, so we'll all get to find out how much of him was me. I'm looking forward to it," Colbert told The New York Times.
Right-wing radio host Rush Limbaugh lambasted CBS's decision to put Colbert in charge of an institution of US media and culture.
"CBS has just declared war on the heartland of America," Limbaugh said. "No longer is comedy going to be a covert assault on traditional American values... Now it's just wide out in the open."
- Merry-go-round -
Letterman's announcement last week was the latest in a merry-go-round of changes bringing a younger generation of hosts to the fore in the US late-night landscape.
In February, 39-year-old Jimmy Fallon took over at NBC's "The Tonight Show" after Letterman's long-time rival Leno, 63, announced his departure.
"Saturday Night Live" star Seth Meyers is NBC's new talkshow hope at 12:30 am, inheriting Fallon's old time slot.
The changes have also involved some geographical rivalry: Leno taped "The Tonight Show" in Los Angeles, but the show moved to New York with Fallon.
That left Jimmy Kimmel as the only major late-night host still on the West Coast. Letterman also tapes in New York.
But tellingly, CBS did not specify where the Colbert "Late Show" will be made, saying the location "will be determined and announced at a later date."
Comedy Central said "The Colbert Report" will end in December.
The exact date of Colbert's first "Late Show" will be announced after Letterman decides on plans for his final broadcasts in 2015, according to CBS.
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"Simply being a guest on David Letterman's show has been a highlight of my career," he 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," he said, referring to Letterman's gap-toothed smile.
- 'Another guy with glasses' -
Letterman said: "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," he quipped.
Letterman, 66, a pillar of American late-night TV talk shows, announced last week that he will leave his "Late Show" studio at CBS next year after a 22-year run.
Colbert -- who got into hot water recently over offensive language about Asian Americans -- has agreed to a five-year deal with CBS, starting after Letterman stands down.
"Stephen Colbert is one of the most inventive and respected forces on television," said CBS boss Leslie Moonves.
Before launching his eponymous show, Colbert spent eight years as a correspondent on Comedy Central's "The Daily Show" with Jon Stewart, which has won 19 Primetime Emmy Awards.
On "The Colbert Report," which has won four Primetime Emmys, Colbert plays a parody of an ultra-conservative talkshow host, although he himself is widely perceived as liberal.
"I won't be doing the new show in character, so we'll all get to find out how much of him was me. I'm looking forward to it," Colbert told The New York Times.
Right-wing radio host Rush Limbaugh lambasted CBS's decision to put Colbert in charge of an institution of US media and culture.
"CBS has just declared war on the heartland of America," Limbaugh said. "No longer is comedy going to be a covert assault on traditional American values... Now it's just wide out in the open."
- Merry-go-round -
Letterman's announcement last week was the latest in a merry-go-round of changes bringing a younger generation of hosts to the fore in the US late-night landscape.
In February, 39-year-old Jimmy Fallon took over at NBC's "The Tonight Show" after Letterman's long-time rival Leno, 63, announced his departure.
"Saturday Night Live" star Seth Meyers is NBC's new talkshow hope at 12:30 am, inheriting Fallon's old time slot.
The changes have also involved some geographical rivalry: Leno taped "The Tonight Show" in Los Angeles, but the show moved to New York with Fallon.
That left Jimmy Kimmel as the only major late-night host still on the West Coast. Letterman also tapes in New York.
But tellingly, CBS did not specify where the Colbert "Late Show" will be made, saying the location "will be determined and announced at a later date."
Comedy Central said "The Colbert Report" will end in December.
The exact date of Colbert's first "Late Show" will be announced after Letterman decides on plans for his final broadcasts in 2015, according to CBS.
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