An award-winning show, that tells the story of Nigerian musician Fela Kuti, opened at the National Theatre (NT) to a standing ovation.
The production, which premiered in New York in 2008, transferred to Broadway last year and won three Tony awards.
Earlier this month it was revealed that the late musician's official biographer was suing the show's producers for breach of copyright.
Carlos Moore is seeking $5m (£3.1m) in damages.
But a spokesman for the show's producers claims Mr Moore had previously supported the production.
Fela! explores the musician's controversial life as an artist and political activist through more than two-and-a-half hours of extravagant song and dance routines.
The musical is set at Fela's final concert at The Shrine in 1978, six months after the death of his mother, Funmilayo (Melanie Marshall).
Fela is played by Sahr Ngaujah, who originated the role in the off-Broadway production.
Fela Anikulapo Kuti, who died in 1997 from an Aids-related illness, was the king of Afrobeat. His pioneering music was a blend of jazz, funk and African rhythms.
Unlike most NT productions, the Fela! musical actively encourages the audience to stand up and dance.
The encore saw the show's artistic director and choregrapher Bill T Jones take to the stage - stripped to the waist - to dance with the cast.
Fela! will be broadcast live to cinemas around the world on 13 January 2011.
The show's executive producers include rapper Jay-Z, and actors Will and Jada Pinkett Smith.