The première took place at the British Film Institute (BFI) on London's South Bank. Also in attendance were Pattie Boyd, The Rolling Stones' Ronnie Wood and Bill Wyman, and Monty Python's Michael Palin, Eric Idle, and Terry Gilliam.
Scorsese made the documentary in collaboration with Harrison's widow Olivia. Living In The Material World follows the former Beatle's life from his Liverpool childhood, charting his musical, spiritual and personal journeys through life.
Olivia Harrison opened up her archives to the director, allowing the use of previously unseen footage, diaries and photographs. A tie-in book, also called Living In The Material World, is published in conjunction with the film's release.
By a force of nature we [she and Scorsese] were guided together. Marty has such a great love of music, I'm really just very fortunate to have him, a great storyteller.
Academy Award-winning director Scorsese spoke of his difficulties in assembling the archive footage alongside interviews with McCartney, Ono and Starr and others.
It's difficult because you may have a great line of dialogue from one interview when he's got a beard and moustache and you cut to another one and you say 'who was the other guy?' We had to go very slowly on this.
Arriving with his fiancée Nancy Shevell, McCartney told reporters that the event brought back plenty of "fond memories".
He [Harrison] was my little mate on the school bus when he was very little. And we were both very little, mind you. But it does bring back a lot of fond memories. He is a lovely boy and he is sorely missed by us all.
The documentary has a limited cinema release around the UK on Tuesday 4 October, with further showings later in the week. The book is published on 3 October, and the DVD and Blu-Ray editions go on general release in the UK on 10 October.