Malins paid £6m for the six-storey Grade II listed period building complete with blue plaque in memory of John Lennon.
The developer will now work with Westminster Council to consider options for future use, including residential apartments on the upper floors with retail at street and lower ground level.
Lauren Atkins, MD of The Malins Group, said: “94 Baker Street has a unique place in the history of The Beatles and we are planning to create the ultimate piece of Beatles memorabilia – a chance to own a slice of the Fab Four’s story.”