NEW YORK — Stephen Colbert will not only be following in David Letterman’s footsteps, he’ll be doing it on the same stage.

CBS said Wednesday that Colbert, who is replacing Letterman as the “Late Show” host next year, will keep the show in New York City’s Ed Sullivan Theatre. Colbert’s debut date is still uncertain, dependent on when Letterman officially retires from late-night TV.

“Tonight” show host Jimmy Fallon already tapes his show in New York, and fellow competitor Jimmy Kimmel at ABC is based in Los Angeles.

New York Gov. Andrew Cuomo said CBS is eligible for up to $11 million in tax credits for keeping the show in New York. The state is also making up to $5 million in grant money available for renovating the theater.