Ministers hope the Whitehall building, in which the likes of Winston Churchill and David Lloyd-George once had offices, will sell for more than £100m.
Defence Secretary Philip Hammond said civil servants would move to the main Ministry of Defence (MoD) building.
He said having defence staff under one roof would save £8m a year.
The first brick of the War Office was laid in 1901 and, by its completion, the Edwardian Baroque building had used 25 million bricks and many thousands of tonnes of Portland and York stone.
Its roof boasted sculptures symbolising Peace and War, as well as Truth and Justice – and Victory.
A parliamentary answer in April 1910 gave the full cost of the “new” War Office as just over £1.2m.
Among the secretaries of state for war who worked there in its early years were Lord Haldane, Lord Kitchener and Winston Churchill, while Lawrence of Arabia was also employed there to create maps of the Sinai region based on his earlier travels.
A young officer posted to the War Office in 1940 recalled being told there had been friction between the armed forces and civil servants – and that he must remember that “not every civil servant based there was a fifth columnist”.
German bombs hit the War Office several times during World War II, killing one person, but the building was relatively unscathed.
It was refurbished in the mid-1980s and reopened in 1992, primarily as the new headquarters of the defence intelligence staffs.
Its current civil servants will move across the road to the MoD's main building next year, after which the historic building – latterly called the Old War Office – will be sold.
With more than 1,000 rooms, 2.5 miles of corridors and a central London location, it could attract interest from property developers and hotel chains, which have already bought other government property being sold off as the coalition attempts to cut costs.
The MoD has also announced plans to sell the abandoned Brompton Road Tube station, which was used as a command bunker for anti-aircraft defences during World War II.