David Letterman will make his first appearance on “The Oprah Winfrey Show” next month, another sign the talk-show titans have buried the hatchet after a rift that lasted more than a decade.

Letterman will tape the interview, a rare appearance on someone else’s show, on Sept. 10 at Madison Square Garden in New York, Winfrey’s production company announced Wednesday.

Their reconciliation began in 2005 when Winfrey appeared on CBS’ “Late Show with David Letterman.” It was Winfrey’s first guest appearance with Letterman, though she twice appeared on his NBC show before the comic jumped networks in 1993.

Letterman frequently joked about Winfrey, and she rejected repeated offers to appear on his program. In 2003, Winfrey told Time magazine she wouldn’t appear with Letterman because she had been “completely uncomfortable” as the target of his jokes.

When Winfrey appeared on Letterman’s show two years ago, she told him, “I want you to know, it’s really over, whatever you thought was happening.” Letterman responded: “Are you sure it’s over?”

The nationally syndicated show will appear live in some markets and will be rebroadcast in others, said a spokeswoman for Winfrey’s Chicago-based Harpo Productions Inc. studios.

On the Net:

“Late Show with David Letterman:” http://www.cbs.com/latenight/lateshow/

“The Oprah Winfrey Show:” http://www.oprah.com