The deal is £120m more than the guide price when the 1.7 acre site was put on the market in September.
The Met Police are moving into a new smaller home at the Curtis Green building on Victoria Embankment which is being transformed by BAM Construction under a £58m contract.
Proceeds from the New Scotland Yard sale will kick-start a major investment in new technology and fund investment in the remaining police estate.
Abu Dhabi Financial Group fought off ten rival bidders in the sale handled by Jones Lang LaSalle.
The developer has a strong track record in London including the 1 Palace Street project adjacent to Buckingham Palace
The Mayor of London, Boris Johnson said: “The Met Police has a unique place in history and they need a home fit for the future, but police budgets are under real pressure.
“The sale of this under-used and outdated building means we can now not only protect that rich heritage, but also fund the new HQ and kit out bobbies with the latest mobile technology to secure the future of the force.
“This landmark deal allows us to preserve the past whilst giving today’s Met a vital cash boost so our officers can go on keeping London safe.”
Jassim Alseddiqi, CEO of Abu Dhabi Financial Group, said: “This will be one of the most important redevelopment projects undertaken in Central London this decade, replacing a world famous headquarters with a world class development.
“With the bid process now complete, we look forward to creating an exceptional new landmark for London.”