The mysterious woman came forward after housebuilder Taylor Wimpey pulled out of its bid to purchase the film studios, The Telegraph reported. Richmond Council had rejected planning permission to convert the historic building into residential homes. Director Steven Spielberg and actor Colin Firth, amongst other celebrities, had spent months campaigning for the safety of the building.
It is believed the woman has promised to maintain the production of films at the business.
The sale is thought likely to take up to four weeks to complete, and is being managed by administrator Gerald Krasner at Begbies Traynor.
The firm entered administration in February this year, after suffering three consecutive years of losses. It was due to be wound down by June if a sale could not be secured.
Some of the more recent films made at Twickenham Film Studios include Warhorse, My Week with Marilyn and The Iron Lady.
Since the identity of the bidder has been kept secret, rumours are circulating as to who she may be.
It is thought JK Rowling was interested in the studio’s future after Harry Potter and the Deathly Hallows was filmed there.