The rulings have been made with both clubs breaking UEFA's earnings rule.
If Chelsea or Villa show fail to show a positive transfer balance by the end of the summer transfer window, they could be prevented from registering players.
Chelsea have been fined €31m and could be fined a further €60m if they do not comply with the rules in the next four years.
Villa have been fined €11m, with a further €15m conditional on compliance in a three-year period.
Chelsea said in response to the ruling: "The club has worked closely and transparently with Uefa to provide a full and detailed breakdown of its financial reporting, which indicates that the financial performance of the club is on a strong upwards trajectory.
"Chelsea FC greatly values its relationship with Uefa and considered it important to bring this matter to a swift conclusion by entering into a settlement agreement."