According to The Stage, producers are looking for singers who rap and hip-hop dancers, who should be in their 20s and 30s and of any ethnicity.
Hamilton tells the story of America's birth and founding father Alexander Hamilton using rap, R&B and hip hop.
Tickets go on sale next month ahead of the show's opening at London's Victoria Palace theatre in October 2017.
Auditions will take place in London, with rehearsals set to begin in August next year.
Producers have said they are not seeing people for the role of King George III, the reigning British monarch at the time of the American Revolution.
The Broadway musical provoked controversy earlier this year by saying they only wanted "non-white" performers to audition for roles.
Hamilton dominated this year's Tony awards, winning in 11 categories including best musical and lead actor.
Creator and original star Lin-Manuel Miranda, who has now left the production, was seen on US TV this weekend hosting Saturday Night Live.
His opening monologue featured a parody of Hamilton song My Shot in which he disparaged Republican presidential candidate Donald Trump.
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Tony-winning Broadway musical Hamilton is to hold open auditions next month for its upcoming West End production.