Both clubs have violated a UEFA rule that relates to the amount of money they earn and spend on players.
As a result, Chelsea and Villa must now show a positive balance in their transfer dealings by the end of the summer transfer window.
If either club fails to meet this requirement, they might not be allowed to register new players.
Chelsea has been fined €31 million, and if they continue to breach the rules in the next four years, they could be fined an additional €60 million.
Aston Villa has been fined €11 million, and if they comply with the rules in the next three years, they will not face any further penalties.
Chelsea released a statement explaining their side of the story, saying they have been transparent and cooperative with UEFA throughout the process.
They emphasized their commitment to working with UEFA and resolving the matter amicably.