Asked if he feared there would be criticism that another investor from overseas has moved into the capital, Mr Johnson said there was no economic difference between "having an investor from Abu Dhabi or having the BP pension fund do this".
The property was put on the market by the Mayor's Office for Policing and Crime (MOPAC) in September, for a guide price of £250m.
The force has raised £215m through the sale of 52 buildings in recent years.
Proceeds from the sale of the 1960s block will be partly spent on new technology to supply officers with tablets, smartphones and body cameras, enabling them to spend more time out on the streets, the Mayor of London's office said.
When completed in 2016, the restructure will save London's police force more than £60m in annual running costs - enough to fund 1,000 officers, the mayor's office added.