Owners the Hinduja Group and OHL Developments were granted planning permission to redevelop the property on the condition that its historic character is not lost and the public can access certain parts of the building at least 10 days each year.
Plans for the 1,000-room Edwardian property – which is located at the junction of Horse Guards Avenue and Whitehall – include the construction of a double-height basement, three new floors and 88 flats.
Cllr Richard Beddoe, senior chairman of planning at Westminster City Council, said: “This exciting development brings another iconic hotel to the heart of London, boosting our economy and further cementing our position as a world-class destination for tourists.
“These plans give this building a new purpose while respecting its place in history.
“The War Office has played a pivotal role in our country’s past and ensuring members of the public had opportunity to visit and experience this iconic building first-hand was a key consideration in our decision.”
Completed in 1906, the Grade II*-listed War Office currently boasts 580,000 sq ft across seven floors.
The building previously served as the headquarters of the British army, playing host to a number of important figures such as former Prime Minister Winston Churchill.
The Hinduja Group and OHL Developments acquired the property on a 250-year lease in March 2016 after it was deemed surplus to requirements by the Ministry of Defence.
The £350m deal was estimated to generate a saving of around £8m-10m per year in running costs.