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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