Abramovich is set to remain Chelsea owner, but will not be involved in decision-making at the Stamford Bridge club.
The senior leadership at the European champions will not change, the Press Association reported.
"During my nearly 20-year ownership of Chelsea FC, I have always viewed my role as a custodian of the club, whose job it is ensuring that we are as successful as we can be today, as well as build for the future, while also playing a positive role in our communities," a club statement said, quoting Abramovich.
"I have always taken decisions with the club's best interest at heart. I remain committed to these values. That is why I am today giving trustees of Chelsea's charitable foundation the stewardship and care of Chelsea FC."
Abramovich, who is from Russia, took over at Stamford Bridge in 2003. He has invested more than $2 billion in Chelsea, transforming the club into one of the most successful in England. The west London club are currently world and European champions.
Abramovich is a former Russian provincial governor who became a steel and metals magnate. He is now a dual Israeli citizen with a net worth estimated at more than $13 billion. Abramovich has not had a British visa since 2018 when a renewal application took longer than usual to go through and was withdrawn.
Chelsea manager Thomas Tuchel had earlier stated that uncertainty over Abramovich's future was weighing on the club ahead of Sunday's League Cup final.
"I would love to take my right not to comment on this until there is a decision made," Tuchel said on Friday. "But we are aware of it and it's distracting us, it's worrying us.
"To a certain degree I can understand the opinions towards the club, towards us who represent that club. I can understand that and we cannot fully free ourselves from it.
"Maybe people understand that me as a coach or the players, we don't have the insight what is really going on. At the moment we don't feel responsible for all this. We feel that it is horrible and there can be no doubt about it."