The iconic theatre, on Leicester Square, is to be redeveloped into a casino and is set to open in 2010.
The move was given the green-light last week, after operator United Gaming Leisure (UGL) won a court appeal granting them the necessary licence.
Gordon Ramsay's restaurant, which will be his 15th in London, would be located on the first floor balcony of the redeveloped venue.
It will be a more casual eaterie, possibly similar to his Plane Food outlet at Heathrow Airport's Terminal 5.
Next to the Ramsay restaurant, there will be a piano bar, 20 gaming tables, a poker room, a members' sports bar and a 105-seat cabaret area.
Simon Thomas, chairman of Hippodrome Casino (the company set up by ULG to run the site), said: "While London has many casinos, they are] mostly small, but almost all are gaming-led, not catering for people who want more.
"The Hippodrome will offer a modern multi-purpose leisure casino where people can go for a whole night's entertainment."
By Kerstin Kühn
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