The building (pictured above), which housed numerous secretaries of state, including Sir Winston Churchill, will go on open market sale shortly, following the appointment of professional agents.
MoD civil servants will move out of the building next year, and all operations will transfer into MoD’s main building, also on Whitehall.
The sale and subsequent move is expected to save around £8m a year, according to the MoD.
The BBC today reported that ministers hope the building will sell for more than £100m, but the MoD declined to comment officially on the potential profit.
The MoD announced earlier this month that it is selling off one of its central London sites at 206 Brompton Road - a former London Underground station - after it was declared surplus to military requirements.
The site - of around 28,000 square feet - is currently occupied by the London University Air Squadron, the London University Royal Naval Unit and 46F Squadron Air Training Corps (Air Cadets).
It is located next to the Grade II* listed Brompton Oratory, Brompton Square, and is just metres away from Harrods.
Defence Secretary Philip Hammond said the money from both sales will be “invested in defence priorities”.
Other historic government properties recently put up for sale include the Admiralty Arch in Trafalgar Square, which was handed over to Prime Investors Capital Limited (PIC) last autumn as part of a 99-year-lease for an agreed premium of £60m.
The building will be transformed into a landmark hotel, with the building remaining in the ultimate control of taxpayers, as the government has retained the freehold of the property.