In a statement published on Saturday morning, the Premier League side said the deal was done and the 'transaction' of the takeover is expected to happen on Monday.
It read: "Chelsea Football Club can confirm that a final and definitive agreement was entered into last night to sell the Club to the Todd Boehly/Clearlake Capital consortium.
"It is expected that the transaction will be completed on Monday. The Club will update further at that time."
Earlier this week, Boehly's takeover jumped its final hurdle with an announcement from the Portuguese government.
The UK government and Premier League had already approved the takeover, but final ratification from the government of Portugal was required for the deal to go through as Abramovich holds a Portuguese passport.
And a statement published on Thursday from the European nation confirmed: "Portugal gave authorisation, this Wednesday night, to the sale of Chelsea Football Club.
"The two responsible national authorities - Ministry of Foreign Affairs and Ministry of Finance - have given the green light to the request received on behalf of Roman Abramovich for a humanitarian derogation, allowing the English club to be transacted.
"The Portuguese authorisation follows the guarantee given by the British authorities that the proceeds from the sale will be used for humanitarian purposes, not directly or indirectly benefiting the owner of the club, who is on the European Union sanctions list. The national position has the agreement of the European Commission."
It means the American billionaire is now the de fecto owner of the Premier League giants, with his £4.25billion deal to buy Chelsea finalised.
This latest news comes 88 days after Roman Abramovich put the club on the market, with LA Dodgers owner Boehly - who has an estimated net worth of £3.5bn - now poised to take the reins at Stamford Bridge.
Abramovich, who took over as owner in 2003, put Chelsea up for sale on March 2, amid Russia's continued invasion of Ukraine.
The 55-year-old was then sanctioned by the UK Government on March 10, with Downing Street claiming to have proven his links to Vladimir Putin.
The Russian-Israeli billionaire has owned Chelsea for 19 years, leading the Blues to 21 trophies and changing the face of English football forever in that time.
Chelsea's sale has required UK Government, European Union and Portuguese government approval due to the sanctions imposed on Russian-Israeli billionaire Abramovich.
The proceeds of Chelsea's sale will be frozen in a UK bank account on completion of the sale.
The UK Government will then need to issue a further licence to allow those founds to be diverted to a new charitable foundation, to aid victims of the war in Ukraine.
Former UNICEF UK chief executive Mike Penrose has been tasked with setting up that foundation, that he believes could 'change the face of humanitarian aid'.
The European Union confirmed its ratification of the Chelsea on Wednesday evening, with commissioner for financial services Mairead McGuinness posting on social media.
"Following detailed discussions between the EU Commission, the UK and Portugal, I am pleased that we have received the necessary guarantees that the sale of Chelsea FC is fully in line with European Union sanctions rules," read a tweet from McGuinness.
"Proceeds go entirely to humanitarian purposes in Ukraine."