The royal guests were met by director Sam Mendes and producers Barbara Broccoli and Michael G Wilson ahead of the screening at the Royal Albert Hall.
Daniel Craig, who has played 007 for a decade, was the first to arrive on the red carpet on Monday night.
He told the BBC: "It's changed my life and I've loved every second of it."
The star also admitted that he "hated" watching himself on screen, but said "I love playing James Bond".
Craig said Mendes was "one of the best directors there is" and that he had enjoyed being "creatively involved from the very beginning".
Other cast members on the red carpet included Naomie Harris, Christoph Waltz, Ben Whishaw, Ralph Fiennes, Andrew Scott, Dave Bautista and "Bond girls" Lea Seydoux and Monica Bellucci.
Bellucci said it was a "great pleasure" to be part of the "amazing tradition" of Bond films.
"It's magic," she said. "It's incredible how James Bond represents so much, not just in England actually, but all over the world."
Scott, who plays a new character called Denbigh, said that the franchise had lasted so well because it kept "reinventing" itself.
The Sherlock star added: "The storyline in this movie is about surveillance and how we're watched constantly. There's a lot of prescient subject matter in the recent Bond films."
Spectre is the first Bond film to open in cinemas on the same day as its premiere.
Mendes said he was delighted that the public were also getting to see the film. "I love the idea that cinemas around the country will be full tonight at the same time as we are doing the royal premiere."
Source: BBC