Los Angeles Dodgers co-owner Boehly had already agreed a £4.25bn purchase of the Blues, with Roman Abramovich’s ownership tenure poised to end after 19 years.
A statement from the Premier League on Tuesday evening read: “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 Government issuing the required sale licence and the satisfactory completion of the final stages of the transaction.”
Boris Johnson’s spokesperson earlier confirmed the government had launched talks with “international partners” to help push the Chelsea sale across the line.
Russian-Israeli billionaire Abramovich has hoped for some time to have been able to satisfy government expectations on how to handle his £1.5bn loan to Chelsea.
The 55-year-old is thought to be confident those demands have been reached, which would finally pave the way for Downing Street to sign off on the sale.
The Premier League statement added: “The Board has applied the Premier League’s Owners’ and Directors’ Test (OADT) to all prospective Directors, and undertaken the necessary due diligence.
“The members of the Consortium purchasing the club are affiliates of the Clearlake Capital Group, L.P., Todd Boehly, Hansjorg Wyss and Mark Walter.
“Chelsea FC will now work with the relevant Governments to secure the necessary licences to complete the takeover.”