Westminster Council granted planning permission to Prime Investors Capital (PIC), last night, for the development, which will include a private members' club and apartments.
The sale of a 99-year lease on the property in October 2012 to PIC for £60m is part of a wider sell-off of unused government buildings in a bid to raise more than £1b for the nation's coffers.
Rafael Serrano, chief executive of PIC, said that he is delighted that Westminster City Council has granted permission to undertake the restoration of the Grade-1-listed building. "We can now give this historical building a worthy and suitable purpose as its designer Sir Aston Webb originally intended and open it up to the public."
Francis Maude, minister for the Cabinet Office, said: The plans will breathe new life into Admiralty Arch, transforming it from unsuitable office space into a publicly accessible landmark that everyone can admire and enjoy.
"Retaining the building's freehold will mean that the public will always have a say in its future and this restoration project will create jobs, boost the local economy and help reduce the deficit."
Originally built as a ceremonial passage from Trafalgar Square to Buckingham Palace, Admiralty Arch is expected to open as a hotel in 2016.
PIC said that it is yet to appoint a management company for the hotel, although it has received interest from "a number of well-known hotel operators".
Admiralty Arch is the second hotel in London to be developed by PIC, following the launch last year of the 85-bedroom Bulgari hotel in Knightsbridge, which is managed by Marriott.