LaLiga announced on Thursday (AEST) that CVC will have a 10 per cent stake in a new business, which is being formed with a focus on the league's commercial ventures. It insisted the agreement does not cover league management or broadcast rights.
The deal will value LaLiga at €24.3bn, with the agreement approved unanimously by the LaLiga Executive Committee and set to be proposed to the league's general assembly.
LaLiga, which controls the top two divisions in Spanish football, said 90 per cent of CVC's €2.7bn investment would be earmarked for its clubs.
However, both Madrid and Barca expressed their disapproval in statements, claiming the clubs were not properly consulted over the deal.
The Clasico giants allege the agreement affects all clubs' audiovisual rights for the next 50 years.
Madrid's statement read, in part: "The clubs have signed over their audiovisual rights exclusively for their sale on a competitive basis for a period of three years.
"This agreement, by way of a misleading structure, expropriates 10.95% of the clubs' audiovisual rights for the next 50 years, in breach of the law."
Barca, who announced on Wednesday that Lionel Messi would not be signing a new contract due to "economic and structural obstacles" wrote: "FC Barcelona feels it is inappropriate to sign a half-century agreement given the uncertainties that always surround the football world.
"The terms of the contract that LaLiga is describing condemn FC Barcelona's future with regard to broadcasting rights.
"FC Barcelona wishes to express its surprise at an agreement driven by LaLiga in which the teams' opinions, including those of FC Barcelona, have not been taken into account. There has not even been a presentation of options offered by other competitors in order to evaluate the pros and cons in a post-pandemic situation in which there are still many questions that are left unanswered."
Madrid concluded: "Real Madrid cannot support a venture which hands the future of 42 Primera and Segunda Division clubs over to a group of investors, not to mention the futures of those clubs who qualify over the next 50 years.
"Real Madrid will convene the Assembly of Representative Members to debate the agreement and discuss the significant loss of equity, unprecedented in our 119-year history."