The plans include an extended terminal, a new aircraft taxiway and parking spaces for planes, as well as upgraded public transport links.
London City Airport estimates the scheme will create 1,600 jobs for staff, together with 500 construction jobs.
Chancellor Philip Hammond hailed the investment as a "vote of confidence in the resilience of our economy."
The planning decision was formally approved by Transport Secretary Chris Grayling and Communities and Local Government Secretary Sajid Javid.
The government said the airport would provide a "generous" compensation package to local residents affected by increased air traffic.
Hammond said: "London City Airport's ambitious growth plans will boost international connections, strengthening the City of London's links to destinations across the world, and send a clear signal that Britain is open for business.
"Making it easier to visit and do business in the City of London will help drive forward our economy and further strengthen the city's status as the world's leading financial centre."
The support for improvements at City Airport comes amid continued delays over a decision on the expansion of Heathrow or Gatwick.
David Cameron was expected to make a decision on the rival expansion projects shortly after the European Union referendum.
But his resignation following the victory for the Leave campaign means the decision has been left for his successor as Prime Minister, Theresa May.
London City Airport's chief executive Declan Collier said: "Today, the new government has shown it is ready to act in the best interests of the British economy.
"Expansion at London City Airport will create more than 2,000 new jobs in east London, add much-needed aviation capacity in the South East, and generate an additional £750m per year for the UK economy.
"As the airport serving by far the highest proportion of business travellers in the UK, who do some £11bn of trade in Europe annually, today the government has sent a strong message that London and the UK are very much open for business.
"I welcome the decision and look forward to delivering new airport capacity for the South East by 2019."
Parveen Thornhill, regional director for UK Trade & Investment London, praised the impact the expansion will have on exporters and small businesses across the South og England.
She said: “Exporters don’t just need good contacts, they also need to be connected to the rest of the world. Better flight routes could well open the door for more businesses to export.
“In 2015 alone, London exported £32bn worth of goods. We work with companies across sectors, from chocolatiers to tech, and there is huge potential for growth in exports of both goods and services."
London Mayor Sadiq Khan also praised the decision on expansion, saying it would bring "much-needed new employment" to the area and show that "London is open to trade and commerce globally."