Colbert to replace Letterman on 'The Late Show'

File photo from May 4, 2011. Stephen Colbert to succeed David Letterman on the Late Show.

CBS said on Thursday that Stephen Colbert will become the host of "The Late Show" when David Letterman retires next year.

Colbert, who hosts "The Colbert Report'' on the cable channel Comedy Central, signed a five-year agreement with the network, CBS' CEO Les Moonves said in a statement.

"I never dreamed that I would follow in his footsteps, though everyone in late night follows Dave's lead," Colbert said in a statement.

The location of the show will be determined at a later date, the network said.

Stephen Colbert to host 'The Late Show': CBS

Comedy Central's Emmy-winning "The Colbert Report" has been a hit since its launch in 2005.

Last week, Letterman announced his plans to exit his show and end an unmatched wee-hours run that began in 1992 when he launched "Late Night" on NBC. He jumped to CBS when Jay Leno, not he, won NBC's "The Tonight Show" upon Johnny Carson's retirement. Leno stepped down from "Tonight" in February, replaced by Jimmy Fallon.

The new late-night faceoff at 11:35 pm ET will consist of Fallon, CBS' Colbert and ABC's Jimmy Kimmel.

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The Associated Press contributed to this story.