NEW YORK — David Letterman ended his 33-year career as a late-night television host Wednesday, ushered into retirement by four presidents who declared “our long national nightmare is over” and saying there was nothing he could ever do to repay his audience.

The show ran 17 minutes over the usual hour, much of it because Letterman took the time to thank the people who worked for him. As the tuxedoed Foo Fighters performed “Everlong”— a song they first played on the “Late Show” when Letterman returned after heart surgery in 2000 — a long montage of photographs from three decades of television history zipped past on the screen.

“The only thing I have left to do for the last time on a television program (is say) thank you and good night,” he said.

Letterman presided over 6,028 broadcasts on CBS and NBC, the transplanted Hoosier making Top 10 lists and ironic humor staples of television comedy and an influence to a generation of performers. True to his self-deprecating style, he said Stephen Hawking estimated that tenure delivered “about eight minutes of laughter.”

Letterman will be replaced in September by Stephen Colbert, who he endorsed by saying, “I think he’ll do a wonderful job.”