The former Beatle, 69, posed for photographs with his fiancée Nancy Shevell on the red carpet, prior to the performance by the New York City Ballet at the David H Koch Theater on the Lincoln Center Plaza in Manhattan, New York City.
McCartney and Shevell arrived at 7.22pm. Also in attendance were his daughter Stella, who designed the costumes for the production, and his son James. The performance lasted 50 minutes contained four movements.
Other stars at the première included actors Sarah Jessica Parker, Naomi Watts, Liv Tyler, Anjelica Huston and Alec Baldwin, and musicians Jon Bon Jovi, Paul Simon, Edie Brickell, Steve Van Zandt and Micky Dolenz.
NYCB conductor Fayçal Karoui gave an introductory speech, in which he thanked McCartney for the music and for working with the ballet company. He discussed the moods of the various movements in the production, and led the orchestra through several snippets to demonstrate.
NYCB's Ballet Master in Chief, Peter Martins, also gave a speech in which he thanked McCartney. He then revealed a surprise, saying that it was a tradition to drink a toast to the composer. A pot of English tea was brought out, and Martins raised a cup to McCartney to great applause.
New York City Ballet was founded in 1948 by George Balanchine. In the early 1970s he started a tradition in honour of Igor Stravinsky: at the opening of a new performance Balanchine would toast the composer with a glass of vodka. Martins' toast to McCartney brought cheering and great applause from the audience.
The dancers took several curtain calls at the end of the hour-long show, and the lead ballerinas were given bouquets of flowers. Stella McCartney was brought onto the stage to take a bow and was given a pink bouquet.
Paul McCartney then appeared on stage. In all there were three curtain calls with various members of the cast and crew, though the last was just him and Peter Martins.
A gala dinner followed the première. It took place in a tent situated at the side of the David H Koch Theater.
McCartney has previously released four albums of orchestral or classical music: Liverpool Oratorio (1991), Standing Stone (1997), Working Classical (1999) and Ecce Cor Meum (2006). The soundtrack to Ocean's Kingdom will be released in October 2011.
Ocean's Kingdom is a collaboration between Sir Paul and NYCB's Ballet Master in Chief, Peter Martins. The pair met in 2010 at the School of American Ballet's Winter Gala, and shortly afterwards began discussing working together.
Like the rest of my generation, I grew up being a huge fan of the Beatles so I was thrilled to meet him. After I got to know him a bit, and knowing of his great love of composing classical music, I asked if he might be interested in doing something for New York City Ballet, and I am ecstatic that he has agreed to write a score for us.
The ballet tells of a love story based in two fantastic worlds - the "pure" ocean kingdom, and the Earth kingdom with its "sort of baddies" who threaten the underwater way of life. According to McCartney, love happens when earth meets water, and "you'll have to see whether the couple make it".
While planning the score for the ballet, McCartney visited the Royal Opera House in London to watch Adolphe Adam's Gisele, danced by the Royal Ballet. He met the dancers and discussed their work, after which he realised that he needed a central theme for Ocean's Kingdom.
Ocean's Kingdom was the first time that McCartney had written an original score for dance. He described the project as "a challenge".
Trying to write something that expressed an emotion was very interesting - so you have fear, love, anger, sadness to play with, and I found that very interesting and challenging but great - I'm really glad I accepted.
I enjoy writing music full stop, so whether it's an orchestra or rock, I immerse myself in it.
I'm a very enthusiastic person so I enjoyed the process - I didn't really find it too difficult. What was interesting was writing music that meant something expressively rather than just writing a song.
I'd seen the great traditional ballets like Swan Lake and The Nutcracker, but I had a very limited knowledge of ballet. But since this project I've obviously started to take notice - I went to see Giselle recently in London and was bowled over by the sheer athleticism of the dancers.
Following the world première, Ocean's Kingdom will be performed four additional times in 2011, on 24, 25, 27 and 29 September, followed by further performances on 19, 21, 24, 27 and 29 January 2012.