The government is expected to approve the takeover within the next 24 hours.
They have received legal guarantees that Roman Abramovich will not benefit from the sale of Chelsea meaning that they can approve the deal.
Sky Sports News understands that the proceeds of the sale will go into a frozen bank account.
The sale of the club must be approved by the Portuguese authorities because of the sanction by the European Union. The deal is expected to be signed on Tuesday.
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The deal will end the 19-year ownership of the club by the Russian billionaire.
Boehly, co-owner of the LA Dodgers baseball team, and fellow consortium member Hansjörg Wyss were at the game.
The news will be a boost for Thomas Tuchel as they have been unable to buy or sell players or negotiate new contracts with players due to the restrictions imposed on Abramovich over his alleged links to Putin.
After Russia invaded of Ukraine on February 24, the owner put the club up for sale.
During the peace talks between Russia and Ukraine, Abramovich suffered symptoms of suspected chemical weapons poisoning and was part of a delegation trying to broker a peace deal.
On March 10, the UK government imposed sanctions on the man, but granted him a special licence to operate.
The talks over the sale have dragged on in recent weeks, with reports that he wanted to repay his loan before he would approve a sale.