The theatre is part of a new planning application to revamp the area around Tottenham Court Road station, which is currently undergoing major redevelopment due to complete in 2017.
The plans, submitted by Crossrail in conjunction with landowners Derwent London, also include a series of shops, offices, flats and nightclubs that would be constructed on Charing Cross Road and Great Chapel Street.
The applications have been submitted to Westminster Council, who have already granted planning permission for the theatre.
Mayor of London Boris Johnson said: “The east end of Oxford Street has long deserved the economic boost, improved public space and glamour these plans will deliver. It will be a gleaming example of the opportunities that will follow the route of this new line, as well as offering the facility to zoom from one side of London to the other at record speed.”
Ian Lindsay, Crossrail Land and Property Director, added: "These development plans will enhance Oxford Street and Charing Cross Road as a thriving cultural and retail destination. The quality of the new commercial space created will help attract major retailers to the eastern end of Oxford Street and boost the wider regeneration of the area."
According to the planning application, the council required that the new theatre have a capacity larger than 250 seats as it considers a venue of smaller size is "unlikely to be viable". A deal is believed to have been struck with Nimax to operate the new Astoria.
The historic Astoria Theatre was originally built as a pickle factory. It was converted to a cinema in 1927, and was more recently used as a live music venue and nightclub until it closed in 2009, prior to planned demolition to make way for the £16 billion east-west rail line.