The Ministry of Defense hopes to get 100 million pounds ($156 million) for the thousand-room building, the BBC reported.
Officials say consolidating the Defense Department in a single building will also save 8 million pounds ($12.5 million) a year.
The baroque building was completed in 1902. Much of the planning for the British military in World War I and World War II was done there by such leaders as Herbert Horatio, Lord Kitchener and Winston Churchill. More junior employees who worked at the War Office included T.E. Lawrence, the future "Lawrence of Arabia."
The building was hit by bombs during World War II but sustained little damage.
With its location near St. James Park, the historic structure is thought to be suitable for conversion to a hotel or luxury housing.
Another World War II landmark, the Brompton Road tube station, is also up for sale. The station was used as a bunker for anti-aircraft artillery during the war.
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