Letterman, who turns 67 next week, made the announcement during Thursday's taping of "Late Show" in New York City. He said he informed CBS president and CEO Leslie Moonves that he will step down when his contract expires in 2015.
"I just want to reiterate my thanks for the support from the network, all of the people who have worked here, all of the people in the theater, all the people on the staff, everybody at home, thank you very much. What this means now, is that Paul and I can be married," Letterman joked, referring to the show's band leader and his sidekick, Paul Shaffer.
Letterman added, "We don't have the timetable for this precisely down. I think it will be at least a year or so, but sometime in the not too distant future; 2015 for the love of God, in fact, Paul and I will be wrapping things up and taking a hike."
The audience clapped and gave him a standing ovation.
His late-night career has spanned more than 32 years and nearly 6,000 episodes. He was the first host of "Late Night" on NBC from 1982 to 1992. Letterman has been the only host of "Late Show" on CBS, which debuted in 1993.