United Leisure Gaming won a case last year, opposed by other casinos in central London, to house a gaming centre at the historic venue.
The plan is to revitalise the venue and restore the Frank Matcham-designed venue to some of its early 1900s glory, but the current owners want it kept as a theatre venue and corporate events space.
London Hippodrome MD Charmaine Haig, who owns the lease with business partner Nick Wright, said the aim was to prevent another historic space being " closed forever".
Currently theatre troupe La Clique inhabits the Leicester Square venue, but in the early 1900s the Hippodrome used to feature water spectacles in a huge tank and performances featuring live polar bears and elephants.
Work on the casino is planned as early as summer.
This news comes after former nightclub Equinox, which is a mere 200 metres from the London Hippodrome, was successfully converted into one of the capital's biggest casinos only two years ago.
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