CBS made its choice, quickly and definitively: Stephen Colbert will succeed David Letterman as the host of its late-night franchise, which Mr. Letterman created when he came to the network in 1993.

The network made the announcement on Thursday, exactly one week after Mr. Letterman said that he would be leaving the “Late Show With David Letterman” after one more year on the air.

Mr. Colbert, the star of Comedy Central’s “Colbert Report,” will be — in one way — an all-new talent for CBS because he will drop the broadly satirical blowhard conservative character he has played for nine years, and instead perform as himself.

Mr. Colbert became the immediate front-runner for the position both because of an increasing recognition of his talent — his show won two Emmy Awards last year — and because he clearly wanted the job. His representation had ensured that he would be available to CBS by syncing his recent contracts with Mr. Letterman’s.