Celebrities including former Spice Girl Geri Halliwell, Oscar-winner Dame Judi Dench, singer Shirley Bassey and pop group B*Witched packed the Lyceum Theatre for the first night.
Sir Tim Rice and Sir Elton John, the duo behind many of the songs, were also there.
Already a critical and box office success on Broadway, Disney's show is based on its own 1994 Oscar-winning cartoon - which has grossed £500m worldwide.
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"It's bold, it's funny, it's unique," said Sir Elton, explaining the appeal of the musical, for which he won an Academy Award for the song Can You Feel the Love Tonight.
But he was quick to credit the show's Tony-winning director, Julie Taymor, for the success.
"Julie has to take all the plaudits, because really it is her vision."
Taymor, who made Broadway history when she became the first woman to win a Tony Award for best director of a musical, was given 15 months by Disney to create the landmark musical.
She adopted Japanese puppetry and Indonesian temple dancing to bring the African savannah to life.
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The 46-strong cast wear African-style masks suspended over their heads to evoke the animals they play.
Walt Disney's chief executive Michael Eisner, also in London for the opening, said Disney had always taken risks and told difficult stories.
"From Bambi to Lion King, we have dealt with serious subjects, and I hope that in the end it is not too frightening," he added.
The Lion King follows the journey of Simba the lion cub who defeats his usurping uncle, the evil Scar, to reclaim his rightful place as king.
For the stage show, Taymor brought in Soweto-born composer Lebo M to give a more African feel to the story. The five musical numbers from the film have now been extended to 15.
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"The show has a personal significance for all of us," said Lebo M, who fled South Africa in its apartheid days and returned only after independence.
"When I left South Africa, I had no political knowledge. It was only in America that I learnt about my culture."
The show is already up and running in Japan with a Canadian production to follow next April, while a Los Angeles staging is expected next October.
And with advance bookings said to have topped £10m and the Lyceum Theatre reported to have been booked for the next five years, The Lion King will give Andrew Lloyd Webber's feline hit Cats "paws" for thought.
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The Lion King
Official London Theatre Guide
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