The takeover is expected to be completed on Monday after Chelsea confirmed an agreement for the record-breaking sale.
A consortium led by US magnate Boehly have spent £4.25billion in order to get their hands on the Premier League club.
Once the deal is signed, sealed and delivered, Abramovich's 19-year reign at Stamford Bridge will officially come to an end.
The Russian-Israeli billionaire led the Blues to 21 trophies - including two Champions League titles - and changed the landscape of football both in England and internationally.
Abramovich put Chelsea on the market on March 2 due to the ongoing conflict in Ukraine. The 55-year-old was subsequently sanctioned by the UK Government, with Downing Street claiming to have evidence of the billionaire's links to Russian president, Vladimir Putin.
In a statement on the Chelsea website, Abramovich said: "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.
"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 20 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.
"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."