NEW YORK (AP) -- Oprah, Dave. Dave, Oprah.The cold war between television titans Oprah Winfrey and David Letterman has thawed to the point where Winfrey has accepted Letterman's invitation to appear on the "Late Show" on December 1.Letterman made the announcement during a taping of his show on Monday. Winfrey's appearance will coincide with opening night of the Broadway musical "The Color Purple," which she is producing."What a big night that is going to be -- not only for us, not only for Oprah, but for Broadway," Letterman said. "You have the big 'Color Purple' Broadway opening, and then right across the street here in this theater, you have Oprah appearing here. I mean, that's what Broadway is all about -- it's a street of dreams."It's Winfrey's first visit to "Late Show," although she was twice Letterman's guest on his NBC show before the late-night comic moved to CBS in 1993.The origin of their "feud" was murky, although Letterman has frequently joked about her through the years. Letterman's failed 1995 stint as Academy Awards host is best remembered for his awkward "Oprah, Uma. Uma, Oprah" introduction.Winfrey told Time magazine in 2003 that she wouldn't go on Letterman's show because she's been "completely uncomfortable" as the target of his jokes."This just gives you an idea of what a big, big star this really is," Letterman said on Monday. "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."Back in 2003, Letterman joked about wanting Winfrey on his show to hold "the Super Bowl of love." Winfrey -- who had sent an olive branch gift of books for Letterman's newborn son -- called his bluff and invited him on her show. He declined."Here's what would happen: I would go on the 'Oprah' show, and I would break down and sob like a little girl ... I don't want to have that happen," he said at the time. "I'd feel ridiculous. I'd never be able to live that down, that Oprah would make me sob."Former Winfrey protege Dr. Phil has been a frequent Letterman guest, offering his own form of "tough love" in a needling relationship.Oprah's appearance is a big boost for Letterman, who has been struggling in the ratings this season and falling further behind his nemesis, NBC's Jay Leno.The timing isn't quite ideal, however: Winfrey will visit the day after the November ratings sweeps period ends.Copyright 2005 The Associated Press. All rights reserved.This material may not be published, broadcast, rewritten, or redistributed.