Stephen Colbert signed off the final episode of The Late Show with special guest Sir Paul McCartney, bringing the programme's historic 33-year run to an end.

On Thursday night's show, Sir Paul and Colbert reminisced about past appearances at New York's Ed Sullivan Theater by The Beatles, and memories of the band touring the US.

The pair closed with a performance of Hello, Goodbye, as The Late Show's crew and staff gathered on stage to take their final bows.

CBS announced the surprise cancellation of The Late Show in July last year, with Colbert hosting 11 seasons after taking over from David Letterman, who had fronted the late-night comedy show since its launch in 1993.

Colbert opened the show with his usual monologue, telling the audience it was going to be business as usual instead of a "special" farewell episode.

Throughout the episode, there was much speculation over who would be Colbert's final guest.

Actors Bryan Cranston, Paul Rudd and Ryan Reynolds were among several celebrity cameos who came out vying for the honour, only to be told they did not make the cut.

A devout Catholic, Colbert had long said he would like to have Pope Leo XIV for his last interview.

But even as he began to introduce his final guest as hailing from "the Vatican", a staffer interrupted to say Pope Leo was refusing to come out of his dressing room.

"We didn't read his whole rider, and we didn't get him his snacks," his staffer said.

The only glimpse the audience had of "the Pope" was an arm reaching out from behind a dressing room door labelled "Pope Leo XIV" and throwing away a hot dog.

"The Pope, who was definitely my guest tonight, has cancelled. We already sent the other stars away. This is terrible," Colbert said. "Who's going to be my last guest now?"

It turns out, Sir Paul happened to "be in the area" and sat down with Colbert to share his thoughts on returning to the Ed Sullivan Theater, and his first impressions when touring the US with the Beatles.

He said the US was "where all the music we loved came from, all the rock 'n' roll, the blues and the whole thing...America was just the land of the free, the greatest democracy".

"Yes, that was what it was. That's what it still is, hopefully," Sir Paul added.

After a rousing performance of Hello, Goodbye, the last moments of the show featured Colbert and Sir Paul backstage, turning off the lights of The Late Show for good.

Outside the Ed Sullivan Theater, fans gathered under The Late Show's glittering marquee one last time with signs of "Thank You Stephen" and "Colbert for President".

"We're just very sad that Stephen's leaving, and it's just going to leave a big hole in America," Sarah Thompson told the BBC. "Because you need to laugh at the end of the day."

Wendy Sloan was in Amsterdam on Thursday morning and booked an eight-hour flight to New York, fighting zero sleep to be here for Colbert's final hurrah.

"I would have really done anything to be here today," she said.

In the days leading up to the show's final taping, a parade of star guests paid tribute to Colbert's more than decade-long tenure at the helm.

Letterman, a vocal critic of CBS's decision to cancel The Late Show, returned last week as one of Colbert's final guests.

The pair reprised a much-loved segment during Letterman's stint as host - throwing furniture and watermelons off the roof of the Ed Sullivan Theater onto a CBS logo.

Steven Spielberg, Tom Hanks, Bruce Springsteen, and Colbert's late night colleagues Jon Stewart, Jimmy Fallon, Jimmy Kimmel, Seth Meyers and John Oliver all stopped by the desk to show their support.

Fallon and Kimmel both announced last week they would not be airing new episodes of their shows on the night of Colbert's finale out of respect.

Colbert had become one of US President Donald Trump's staunchest critics on late-night TV, and some questioned whether the decision to axe his show may have been due to political pressure.

But CBS said last year that the move was "purely a financial decision against a challenging backdrop in late night [television]" and "is not related in any way to the show's performance, content or other matters".