WASHINGTON (TIP): Closing out a TV career that has spanned more than three decades and influenced a generation of comedians, David Letterman will end his record-setting run as a late-night star on May 20, CBS announced December 10. Mr. Letterman, host of “Late Show With David Letterman,” has had a 32-year run, including a previous show on NBC, the longest tenure of any late-night host in television history. He announced last April that he would finish his CBS show at the end of his current contract, which concludes at the end of July. His exact departure date was left unsettled, and CBS let him decide when he would perform on “Late Show” for the last time.

But the timing does affect the network’s plans for its succession to the new host, Stephen Colbert. No date has yet been set for Mr. Colbert’s premiere on CBS, though he will leave his current show, “The Colbert Report,” on Comedy Central, next week. Several executives involved in the transition have predicted that Mr. Colbert would start on “Late Show” next September. That would leave more than three months between Mr. Letterman’s departure and Mr. Colbert’s debut.

So far, CBS had not said how it will fill that hour in the interim. Chris Ender, a CBS entertainment spokesman, said Wednesday that the network had nothing to announce yet, though it has “discussed a variety of options” to fill the time period. CBS faced a similar situation with its 12:35 a.m. show. Craig Ferguson, who has starred on “The Late Late Show” since 2005, is finishing his run Dec. 19. His replacement, James Corden, will start in March. CBS has announced a roster of guest hosts in the interim.