The sale price of 2.5 billion pounds ($3.1 billion) for the reigning Club World Cup winner and 2021 European champion is the most lucrative ever for a sports team worldwide but Abramovich cannot receive the proceeds, which he hopes will go to a foundation for the victims of the war.
A further 1.75 billion pounds ($2.2 billion) has been committed to invest in Chelsea's teams and stadiums after two months of rapid negotiations to sell the west London club since Russia invaded Ukraine.
After several rival bids were rejected, Chelsea said on Saturday that buyout terms were agreed with a consortium that features Boehly along with Dodgers principal owner Mark Walter, Swiss billionaire Hansjorg Wyss and funding from private equity firm Clearlake Capital.
The Premier League must approve them as the new ownership and the government has to sign off under the terms of the license that allows Chelsea to continue operating as a business through May 31 while being one of Abramovich's frozen assets.
Abramovich has said he would write off loans of more than 1.5 billion pounds ($1.9 billion) to Chelsea but that has been complicated by the sanctions put in place by the British government as part of a crackdown on wealthy Russians with ties to President Vladimir Putin. Abramovich's side positioned him as a potential peacemaker but that trail has gone silent publicly in recent weeks and the billionaire has not condemned the war.
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Chelsea, whose ability to sell match tickets and commit to new player spending has been hampered by the sanctions, expects the sale to be completed by late May.
"Proceeds will be deposited into a frozen UK bank account with the intention to donate 100% to charitable causes as confirmed by Roman Abramovich," Chelsea said in a statement.
Boehly is already in London and attended Chelsea's Premier League match on Saturday against Wolverhampton at Stamford Bridge. Thomas Tuchel's team is third in the standings with four games remaining. The title is out of reach but Champions League qualification is nearly secured.
"Not relieved," Tuchel said of the prospective sale, "but it gives us an outlook if terms are agreed, and hopefully the process will be streamlined and go forward as soon as possible. Good news."
Chelsea has the smallest and most dated stadium of the Premier League's most successful clubs, with plans for a rebuild of the 41,000-capacity venue put on hold by Abramovich in 2018 as British-Russian diplomatic tensions deepened.
Chelsea said the 1.75 billion pounds committed will be in funding investments in Stamford Bridge, the academy and the women's team, which can win its league title on Sunday.
Boehly is part owner of the Los Angeles Dodgers MLB franchise and he also has minority stakes in the NBA's Los Angeles Lakers and WNBA's Los Angeles Sparks.
The challenge will be maintaining the expectation of regular trophies produced under the expensive transformation of Chelsea, with 21 collected in 19 years.
Chelsea had won the league only once - in 1955 - when Abramovich bought the club in 2003. Helped by expensive signings, the club won the Premier League two years later and has added four more since then, most recently in 2017.
There is increased competition from wealthy owners to buy and retain players. In England alone, Manchester City has benefited from Abu Dhabi investment since 2008 and Newcastle was bought by Saudi Arabia's sovereign wealth fund last year.
No details have been provided about the future day-to-day leadership of Chelsea, which was the first Premier League club to benefit from a mega-rich foreign investor in 2003.
Boehly, who studied at the London School of Economics, co-founded the Eldridge Industries investment firm in 2015 and serves as its chairman and CEO. The private holding company has investments in over 70 businesses, including in sports, entertainment and media.
Besides the Los Angeles teams, Boehly has minority ownership stakes in the esports organization Cloud9 and DraftKings, an American fantasy sports wagering company.
He is chairman of Security Benefit, a retirement solutions provider based in Topeka, Kansas, and MRC, an entertainment company that funds and produces film and television programming, including major shows such as the Golden Globes, the American Music Awards and Billboard Music Awards.
MRC's other holdings include Penske Media, which owns Billboard, Rolling Stone, Variety and the Hollywood Reporter.
Before he co-founded Eldridge, Boehly was president of Guggenheim Partners. Walter, who teamed up with Boehly to buy Chelsea, is CEO of the financial services firm.
Their first chance to see Chelsea win a trophy is next Saturday in the FA Cup final. Liverpool is the opponent at Wembley Stadium.