The US billionaire agreed terms for the purchase of the European champions for £4.25b in early May.
Outgoing owner Roman Abramovich put the club up for sale back in March for alleged links to Russia president Vladimir Putin, who is leading an invasion of Ukraine.
Abramovich had his assets frozen by the UK government and Chelsea have been operating under a special license ever since.
The Premier League and UK government approved the sale earlier this week.
"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," a statement from the club read.
"It is expected that the transaction will be completed on Monday. The club will update further at that time."
Abramovich released a statement thereafter, expressing his satisfaction with the sale process and wishing the club best of luck.
The statement began: "It has been nearly three months since I announced my intention to sell Chelsea FC. During this time, the team have worked hard to find the right custodian for Chelsea FC that would be best positioned to successfully lead the club into its next chapter.
"The ownership of this club comes with great responsibility. Since I came to Chelsea nearly twenty years ago, I have witnessed first-hand what this club can achieve. My goal has been to ensure that the next owner has a mindset that will enable success for the Men’s and Women’s team, as well as the will and drive to continue developing other key aspects of the club, such as the Academy and the vital work of Chelsea Foundation.
"I am pleased this search has now come to a successful conclusion. As I hand over Chelsea to its new custodians, I would like to wish them the best of success, both on and off the pitch.
"It has been an honour of a lifetime to be a part of this club – I would like to thank all the club’s past and current players, staff, and of course fans for these incredible years.
"I am proud that as a result of our joint successes, millions of people will now benefit from the new charitable foundation which is being established. This is the legacy which we have created together.
"Thank you. Roman."
Abramovich took over Chelsea in the summer of 2003 and has injected over £1bn into the club, winning every major club honour available in that time including five Premier League titles, two UEFA Champions Leagues and two Europa Leagues.
