The announcement was made by the veteran late-night TV host during a recording of Late Show with David Letterman, CBS added.
David Letterman, who will be 67 next week, began hosting the show on CBS in August 1993, after leaving the rival NBC network.
He began his TV career in 1978 on the CBS variety series Mary, starring Mary Tyler Moore.
David Letterman’s show has since won a host of TV awards.
During the taping of Thursday’s show, David Letterman said he had informed his CBS bosses that he would step down in about a year’s time, when his current contract expires.
The news comes nearly two months after Jay Leno retired as host of NBC’s The Tonight Show.
Correspondents say both Jay Leno and David Letterman had seen their ratings fall as rival TV presenter Jimmy Kimmel on ABC’s Jimmy Kimmel Live gained popularity with a younger audience.
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