Inspired by the book, The Man Who Fell To Earth, the show premiered last November in New York Theatre Workshop - just a few weeks before Bowie's death in January.
Bowie co-wrote the show with Irish playwright Enda Walsh, the award-winning writer of Once.
It will run at the Kings Cross Theatre from 25 October to 22 January 2017.
Reprising their roles from the original New York production are Michael C Hall, who starred in hit TV series Dexter, Michael Esper and Sophia Anne Caruso.
Telling the story of a human-looking alien who comes to Earth, the production is directed by Ivo van Hove, the Belgian director behind the acclaimed A View From the Bridge, starring Mark Strong, which ran in London and New York.
When it opened in New York, The Guardian described Lazarus as "unapologetically weird... and oddly intriguing".
Rolling Stone praised the show as a "surrealistic tour de force."
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Lazarus, a new stage musical featuring the songs of David Bowie, is to open in London this autumn.