Khan said in a statement on Monday that he was confident the 500 million-pound redevelopment would produce "a jewel in London’s sporting crown" and attract visitors and fans from around the world.
"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," he added.
Planning permission was granted by the local council in January but it was subject to the mayor's approval.
Premier League leaders Chelsea said Khan's decision was a significant step towards the new stadium, which currently has a capacity of 41,600, but some hurdles remained.
"Further steps lie ahead, both during and after the planning process, before construction work can commence," Chelsea said on the club website (www.chelseafc.com).
The new stadium has been designed by Swiss-based architects Herzog and de Meuron, whose other work includes Bayern Munich's 75,000-seat Allianz Arena and Beijing's "Birds Nest" Olympic Stadium.
The current ground dates back to 1877 and has been home to the west London club since 1905.
Chelsea's three main London rivals either have or are building larger stadiums than their previous homes.
Arsenal play at the 60,000 capacity Emirates Stadium, Tottenham Hotspur are building a new White Hart Lane ground with a similar capacity and West Ham United now play in the London Stadium, built for the 2012 Olympic Games.
($1 = 0.8161 pounds)
(Reporting by Alan Baldwin, editing by Ed Osmond)
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