Real and Barca are fiercely opposed to the deal, which was initially worth around 2.7 billion euros for a 10 per cent stake in the top two Spanish leagues.
Given the stance of Spain’s Clasico rivals, CVC modified its original proposal shortly before the vote, allowing clubs to take part on a voluntary basis.
If Real Madrid, Barca and Athletic Bilbao choose not to join the deal, the investment is likely to total between 2.1/2.2 billion, LaLiga president Javier Tebas told a news conference.
Despite the approval by 38 out of LaLiga’s 42 clubs, the deal still faces legal risks.
CVC sought to pour money into LaLiga in exchange for nearly 11 per cent of its revenue from television rights over the next 50 years.
The league has argued the deal, called “Boost LaLiga”, would strengthen clubs and give them funds to spend on new infrastructure and modernisation projects, as well as increasing how much they can spend on players’ salaries.
Real Madrid are planning to launch civil and criminal lawsuits against LaLiga’s Tebas and CVC Capital’s chief Javier de Jaime Guijarro over the planned deal.
Additional reporting by Reuters.