Mountgrange and Prupim, the firms behind the plan, named One West Regent Street, are expected to convert the building to office space by the end of 2014. The building backs on to the new Buchanan Galleries extension, and will be able to offer 147,000 sq ft of office space.
The art deco building was opened in 1943, and in its 1960s incarnation as the Paramount, was a music venue that drew the biggest stars of the day, including Roy Orbison, Dusty Springfield and Cliff Richard.
It later became an Odeon cinema, which closed in 2006, and has been out of use since. The building is currently owned by Duddingston House Properties, which last November secured planning approval for an 11-storey tower on the site.
The firm had planned its own £80 million facelift project for the building, comprising an office and leisure development, but was unable to go ahead with it due to the economic climate. However, it will retain the front foyer scetion of the building and is thought to be looking for a leisure company to develop it.
Theatre producer Sir Cameron Mackintosh, who produced hits including Oliver!, Les Miserables and The Phantom of the Opera, had announced that he wanted to save the landmark building, using his own money to turn it into a 2,000-seat theatre.