The stadium will be built on the site of their existing Stamford Bridge ground and will see the capacity increase from 41,600 to 60,000.
The Premier League club’s proposal for a new stadium were unanimously approved by Hammersmith and Fulham Council’s planning committee back in January.
Chelsea’s development plans include a contribution of £3.75m towards affordable housing in the borough of Hammersmith and Fulham as well as a £12m investment in community activities.
“London is one of the world’s greatest sporting cities and I’m delighted that we will soon add Chelsea's new stadium to the already fantastic array of sporting arenas in the capital,” said Mr Khan.
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“Having taken a balanced view of the application, I’m satisfied this is a high-quality and spectacular design which will significantly increase capacity within the existing site, as well as ensuring fans can have easy access from nearby transport connections.
“I’m confident this new stadium will be a jewel in London’s sporting crown and will attract visitors and football fans from around the world.”
Mr Khan’s announcement follows support for fellow London football clubs AFC Wimbledon and Millwall over the future of their stadiums.
Chelsea’s new stadium has been designed by renowned architects Herzog and de Meuron, who also helped to create the iconic Bird’s Nest Olympic Stadium in Beijing and the widely acclaimed Allianz Arena in Munich.