The king of late-night television, David Letterman, has brought the curtain down on a 33-year career in an emotional final show packed with jokes and farewells from US presidents, Hollywood stars and devoted fans.

The last-ever Late Show with David Letterman brings to an end an American cultural institution that had been watched by millions, and an extraordinary career that had inspired a generation of comedians.

The finale opened with a bang with former US presidents George H. and George W. Bush and Bill Clinton, as well as President Barack Obama, filmed repeating one after the other, “our long national nightmare is over”.

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“Letterman is retiring,” Mr Obama said, standing shoulder to shoulder with the 68-year-old comedian in a pre-filmed segment.

“You’re just kidding right?” deadpanned Letterman to a no-nonsense shrug from Mr Obama.

The show featured gags at Letterman’s expense, jokes poking fun at celebrity and play-back highlights of years gone by.

Hollywood stars Alec Baldwin, Steve Martin, Bill Murray and Jim Carrey, and comedians Jerry Seinfeld and Tina Fey led 10 stars who performed the bit “Top 10 things I’ve always wanted to say to Dave”.

Their pithy one-liners paid tribute to the caustic and at times grumpy humour of the veteran broadcaster, the longest-serving night time US talk show host, who has been on air since getting his first show on NBC in 1982.

“Thank you and goodnight,” Letterman said at the end of what was the 6028th television show of his career.

“Thank you for everything, you’ve given me everything.”

He also gave thanks to wife Regina and their 11-year-old son Harry who were in the audience.

Rock giants Foo Fighters played out the show to roars from the jubilant crowd at the Ed Sullivan Theater in New York.

Meanwhile, Bill Murray was under a lot of pressure as Letterman’s final guest on the Late Show.

But when Murray is called on to perform, Murray delivers.

The 64-year-old made quite the entrance on the beloved host’s second last episode, arriving in a giant cake and bursting out of it.

Murray didn’t let the fact he was covered in icing deter him from enthusiastically hugging Letterman and doing laps around the studio, sharing the love.

He then swigged from what looked to be a giant bottle of vodka.

Murray was the perfect choice for Letterman’s last interview, after being his first guest on the debut episode of NBC’s Late Night with David Letterman in 1982.

The real fun happened after the interview, however, when Murray crashed MSNBC’s Last Word, falling off his chair.

Seemingly drunk, he then told host Lawrence O’Donnell exactly what he had for dinner.

“I just did the Letterman show then went to dinner. Had oysters, rose wine, red wine, then duck and some green grass-fed hanger steak,” Murray slurred.

“Then rushed here to do your show just because Jim said you wanted me to come on the show.”

Speaking about the incident on The View the next day, host Whoopi Goldberg said she believed the whole thing was another example of Murray’s brilliant acting skills.

“I’m not buying Bill Murray drunk,” Goldberg said.

“Listen, right on the nose baby, [he’s] a much better actor than people realise. People forget how good he is.”

Murray wasn’t all fun and games, taking a moment to celebrate Letterman’s immense talents.

“If you’ve been watching there’s amazing amount of power in the room — there’s a lot of emotion in the room,” Murray told O’Donnell.

“Dave is at some incredible level of capability right now.

“People come out [on stage] and they can do anything and he just floats above everything. He’s really in a different plane than the rest of us right now.”

– with AAP