The deal is yet to be signed off by the British government before it can be completed.
The Premier League board has announced it had approved Todd Boehly's proposed takeover of Chelsea from Russian billionaire Roman Abramovich who was sanctioned by the British government.
A Premier League statement said on Tuesday: "The Premier League Board has today approved the proposed takeover of Chelsea Football Club by the Todd Boehly/Clearlake Consortium."
"The purchase remains subject to the British Government issuing the required sale licence and the satisfactory completion of the final stages of the transaction."
A consortium led by Boehly, a co-owner of baseball's Los Angeles Dodgers, had already agreed a $5.3 billion deal to buy the Premier League club from owner Abramovich on May 7.
Russian billionaire Abramovich put Chelsea on the market in early March, just before he was sanctioned by the British government following Russia's invasion of Ukraine.
But earlier on Tuesday, a spokesman for Prime Minister Boris Johnson confirmed the government were working with the club over the deal.
"We are working closely with Chelsea to progress the sale," the spokesman said.
"We are holding intense discussions with the relevant international partners to get the necessary approvals and we will set out further details as soon as we can."
The deal has dragged out as the British government makes sure that Abramovich, who was sanctioned over his links to Russian President Vladimir Putin, does not profit from the enforced sale of the club.
Chelsea has been operating under a government license since Abramovich’s assets were frozen in March and it expires on May 31.