President Trump has been talking about the emergency facility beneath what was once the East Wing, details of which are usually kept secret, as he tries to justify his renovation.
The board had been expected to vote to approve the project last month, but it was delayed after about 32,000 mostly negative comments rolled in from across the country.
Will Scharf, who was appointed by President Trump as the chairman of the National Capital Planning Commission, at a meeting to approve the White House ballroom plans on Thursday.