The club have been transformed from Premier League also-rans into a trophy-winning machine under the Russian billionaire, winning 19 major trophies since he took charge in 2003.
AFP Sport looks at the tough job that lies ahead for the incoming Chelsea owners.
Stabilise the squad
Chelsea have been operating under a special licence since sanctions were imposed on Abramovich by the British government in March — a week after he announced he was selling the club following Russia’s invasion of Ukraine.
As a result of the restrictions, the Blues were not allowed to offer new contracts to existing players and effectively faced a transfer ban.
Defenders Antonio Rudiger and Andreas Christensen are set to join Real Madrid and Barcelona respectively on free transfers and will need to be replaced.
The futures of Cesar Azpilicueta and Marcos Alonso must be resolved, while Blues boss Thomas Tuchel is reportedly keen to plug the defensive gaps with a deal for Sevilla’s Jules Kounde.
Chelsea must also weigh up whether to stick with their current roster of forwards or sell players to create space for new arrivals.
Romelu Lukaku arrived as the club’s record signing last year but proved inconsistent after a positive start to the season.
On the bright side, Abramovich’s lavish spending means he leaves behind a competitive squad, which just a year ago beat Manchester City to win the Champions League.
They were beaten finalists in the League Cup and FA Cup this season and finished third in the Premier League, ensuring qualification for Europe’s top club competition again.
One of the top priorities for Chelsea’s new owners is likely to be redeveloping Stamford Bridge into a stadium worthy of one of Europe’s elite clubs.
Abramovich shelved plans for a £1 billion redevelopment in 2018 during another dispute with the UK government over his visa.
Stamford Bridge’s capacity of 42,000 lags well behind Premier League rivals Manchester United, Manchester City, Liverpool, Arsenal and Tottenham.
Spurs’ £1 billion home, completed in 2019, has become a sporting hub in the English capital, hosting major boxing, rugby and NFL events, as well as concerts and conferences.
Boehly’s track record of both sporting success and stadium redevelopment as a co-owner of baseball’s Los Angeles Dodgers gave his bid credibility to go with the major funding behind it.
Investment in the stadium was reportedly a key part of the consortium’s pitch to American bank Raine, who oversaw the sale process.
A bigger ground will also be part of the long-term strategy to drive revenue and recoup the huge outlay to buy the 2021 European champions.
Chelsea fans will be relieved that their club at last has a new owner after three months of paralysing uncertainty.
But they will be anxious that Boehly and his consortium rebuild the club’s image after a torrid 12 months following the European Super League debacle and the sanctioning of Abramovich.
Chelsea were one of 12 clubs who last year signed up to the proposed breakaway competition, which was quickly scrapped after a deluge of fan fury.
The club’s reputation has also been tarnished by sanctions imposed on Abramovich by Britain and the European Union.
The billionaire was described by the UK government as part of Russian President Vladimir Putin’s inner circle when it imposed an assets freeze in March.
Fans of the west London club will hope the new consortium is able to continue to deliver the sustained success at Stamford Bridge they are used to, keenly aware of their rivals’ differing experiences under US owners.
American-owned Manchester United and Arsenal have struggled to compete at the top end of the Premier League in recent years, with the Glazer family at United a target for vitriolic protests from fans.
On the other hand Liverpool, owned by Boston-based Fenway Sports Group, have been hugely successful under manager Jurgen Klopp.