A source close to the deal said it would value the whole of the club at approximately 2.5 billion euros.
The deal marks the latest venture into sports by private equity firms, attracted by their stable and predictable revenue streams.
The club's CEO Miguel Angel Gil Marin and President Enrique Cerezo will remain in their roles and as shareholders, Atletico said, and the investment is expected to be completed in the first quarter of 2026.
Sources told Reuters in September the US firm sought to take control of the club by acquiring part of the stakes owned by Gil Marin, Cerezo, and, possibly, from investment fund Ares Management.
Until now, Atletico HoldCo held about 70% of the club, with Gil Marin, Ares and Cerezo owning 50.8%, 34% and 15.2%, respectively. Quantum Pacific held 27.8% outside the group.
"We are equally excited to remain minority investors and continue providing strategic support as the club builds on its momentum," Ares Sport's co-head and director on Atletico HoldCo's board, Jim Miller, told Reuters.
A&O Shearman acted as legal counsel to Apollo Sports Capital. ECIJA acted as legal counsel to Gil Marin and Cerezo.