McCartney was joined on the blue carpet by Beatles bandmate Ringo Starr, John Lennon's widow Yoko Ono, and Olivia Harrison, widow of George.
"We're getting great memories obviously of playing with John and George," McCartney told reporters.
"So that's very emotional and very special to see that again."
McCartney revealed that he was wearing the same jacket as he had worn at the premiere of The Beatles movie A Hard Day's Night in 1964. He was joined at the premiere by his wife Nancy Shevell and daughter, fashion designer Stella McCartney, while Starr was accompanied by his wife Barbara Bach.
Starr described the Beatles' lasting fame as "beautiful". "People love the Beatles," he said. "We happen to be two of them and here we are."
Other guests at the premiere included the film's director, Ron Howard, Madonna, and TV presenter and pianist Jools Holland.
Eight Days a Week, which mixes archive footage with new interviews with McCartney and Starr, chronicles the Fab Four's rise from Liverpool's Cavern Club to the stadium circuit in the US.
Fans see The Beatles at work in the studio and remastered performances, including their legendary Shea Stadium show in New York, the first rock concert played to more than 55,000 people.
While there are plenty of laughs, the film also examines the impact of fame on the band and how The Beatles railed against segregation at certain US venues.
Olivia Harrison took time on the night to pay tribute to Oscar winner Howard's work on the film.
"We were privileged to have Ron Howard making this film," she said. "He's a great storyteller and I think he's learned a lot too."
She said it was "sweet" that some of the home movie footage in the film is from her late husband's 8mm camera.