The elusive Oprah Winfrey, who has been the object of David Letterman’s comedic affection and frustration, has been booked to appear on CBS’s “Late Show With David Letterman” Thursday, Dec. 1, the night the queen of all media’s musical version of “The Color Purple” opens on Broadway.

Mr. Letterman announced during the “Late Show” taping for Monday night that his long-running campaign to cajole or heckle Ms. Winfrey into agreeing to return to his show had finally paid off. “This just gives you an idea of what a big, big star this really is,” he said to his audience. “She’s huge. Put bygones behind us, the water under the bridge, over the dam, wherever water goes — standing in your basement — she’s going to be here on this show and it’s going to be fantastic.”

Ms. Winfrey last appeared on Mr. Letterman’s “Late Night With David Letterman” show on NBC in the 1980s.