Winfrey was Oscar nominated for her role in The Color Purple

She had said her two previous stints on his former NBC late night show in the 1980s had left her feeling "like the butt of his jokes".

Letterman, now on CBS, said it was a time to "put bygones behind us".

Winfrey is co-producing a musical of The Color Purple, which opens on Broadway on 1 December.

Her appearance on his show is due to take place on the same evening. It follows several requests from Letterman.

In 2003, she told Time magazine she would never go on his show again.

Letterman has been a late-night fixture for more than 20 years

At one point, Letterman even jokingly suggested that he and Winfrey could patch up their differences in a "Super Bowl of Love".

Winfrey turned the tables on Letterman in December 2003 by inviting him to appear on her daytime show, an offer he acknowledged but never took up.

Talking of Winfrey's forthcoming appearance, when she will chat about her new Broadway venture, Letterman said: "What a big night that is going to be - not only for us, not only for Oprah, but for Broadway."