Developer the Malins Group is also main contractor on the job which will start immediately.
Malins paid £6m for the six-storey 8,390 sq ft Grade II listed building on Baker Street last year.
The firm has now secured permission from Westminster City Council for a change of use to residential on the upper floors of the building, with retail at street and lower ground level.
Lauren Atkins, MD of The Malins Group, said: “94 Baker Street is destined to become one of the capital’s most famous residential addresses.
“The building has a unique place in the history of The Beatles and we aim to preserve its fascinating heritage.
“We will be launching sales of the apartments on the 45th anniversary of the closure of the Apple Boutique and move of Apple Corps and the 50th anniversary of the formation of the Beatles.
“We have some great plans for the interiors – exuberant, imaginative, with a few Avant-garde touches- to capture the spirit of the Fab Four.”
As well as the base for The Beatles record empire in the late 1960s, the Apple Boutique was opened at street level selling clothes and accessories.