New York’s status as the center of late-night television was reinforced on Wednesday after CBS announced that its “Late Show," which under David Letterman has been based in New York since 1993, will remain in the city when Stephen Colbert steps in as host next year.

CBS’s chief executive, Leslie Moonves, and Gov. Andrew Cuomo jointly announced the decision. They also said the show would stay in its landmark Broadway home, the Ed Sullivan Theater, guaranteeing the continuation of about 200 jobs related to the show.

The decision had been widely expected since CBS announced in April that Mr. Colbert, the Comedy Central star, would be Mr. Letterman’s successor. But CBS was able to strike a favorable tax deal to ensure that the show would not move to Los Angeles, the other potential home for a late-night series. CBS will be eligible for at least $11 million in tax credits over the next five years, as well as $5 million more in state grants to cover renovations for the theater.

More significantly, there had been little doubt that the show would stay because Mr. Colbert had privately expressed his strong desire to keep the show in New York, near his home in New Jersey. Like Jimmy Fallon, who moved NBC’s “Tonight” show back to the city in February, Mr. Colbert has long been considered a “New York act.”