The decision was made by the Planning Inspectorate.
The extension will transform the airport experience and provide capacity to accommodate growth towards the airport’s approved limit.
The scheme will add a three-bay extension to the back of the terminal building, extending it by 16,500m2.
It will create a more spacious departure lounge, with additional seating, a greater choice of shops, bars and restaurants, state-of-the-art check-in desks, increased baggage capacity and a larger security hall with more security lanes equipped with next-generation scanners.
The project will improve every step of the airport journey, from when passengers check in on departure through to when they arrive at immigration.
Stansted has been London's fastest recovering airport, serving more than 27 million passengers in the last 12 months, and has now entered a phase of growth.
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The extension will enable the airport to improve its capacity at busy times and provide the extra space required to accommodate forecast growth.
Gareth Powell, London Stansted’s Managing Director, said: "Our plans will transform the airport experience for everyone connected with London Stansted, so today’s decision by the Planning Inspectorate to approve our scheme is excellent news for our passengers, colleagues, airport partners and the region we serve.
"Stansted is now entering a new phase in its history, as we look to serve more passengers than ever before. Our unique and growing route network, and easy access to and from London and the east of England, is a fantastic platform to build on. We know Stansted will have a critical role to play in serving the future capacity needs of London.
"Being a single terminal airport enables us to offer the millions of passengers who choose us each year a simple, efficient and reliable experience when they fly. This is something they clearly value and enjoy when choosing which airport to use, so they can be confident our plans will build on this success and make every airport journey even better in the future.
"Stansted is a national and regional asset, and our investment plans are not only an exciting prospect for our passengers and colleagues, they will also boost our competitiveness within the London aviation market, which in turn will support economic growth, jobs and vital international connectivity for London and the East of England.
"Our aim is to be the airport of choice for even more passengers, and we are confident we can achieve that goal by further enhancing our facilities and attracting even more airlines to the airport to provide the best range of destinations."
