Contracts have been reportedly exchanged between the corporation and Axa Investment Managers for the Hertfordshire site, which includes seven stages, as well as office, workshop, and post-production facilities.
That being said, EasEnders will still be filmed on the site, as the BBC have agreed to lease part of the studio campus for 25 years.
While the value of the sale has yet to be revealed, the BBC are currently looking to raise £500 million in annual savings. A BBC news report had stated that the corporation were seeking £70 million.
Chief financial officer for the BBC, Alan Dicksen has said that this sale is part of an ongoing review of their property portfolio, as they aim to provide the best value for licence fee payers.
"As part of the sale, the EastEnders site has been secured on a long-term lease and Elstree will continue to be the home of Albert Square," he said. "Moreover, AXA's investment ensures the Elstree site remains a fantastic asset for the UK's creative economy".
The BBC had acquired these studios in 1984, after the Elstree Studios Centre had been converted from a film studio for Neptune Films to a television studio in 1960.
Several iconic movies were filmed in the wider Elstree Studios, including Star Wars. The studio is one of the world's leading film and television production campuses in the world.
Speaking on the sale, John O'Driscoll global co-head of real estate at AXA IM Alts, said that company intends to continue the legacy of producing "celebrated films and television series".
"With the signing of BBC Elstree Centre we will be acquiring one of the oldest working TV and film studios in the UK, with a history dating back almost 110 years," he said. "The structure of the transaction allows the BBC to continue its production on the site for at least another 25 years, while providing us with the opportunity to invest in the site to create new world-class studios".
Mr O'Driscoll also explained how the move was "underpinned by increasing demand from an ever-broader array of production houses, content creators and broadcasters.
He also added that this was coupled with a limited supply of high-quality modern film and production space, "particularly in and around London where new construction is hindered by a lack of available land in the right locations".
