Apollo Sports Capital agreed in November to become the majority shareholder in the top-tier club.
As part of the transaction, the Quantum Pacific Group will retain nearly all of its previously-held stake as the second-largest shareholder, the club said in a statement.
A source with knowledge of the deal told Reuters that Quantum Pacific will own a stake of around 25% in Atletico after the deal.
The new board will include five directors from Apollo, two from Quantum Pacific and A&O Sherman partner Antonio Vazquez-Guillen, the club said.
Former Atletico player and World Cup winner David Villa will also join the board.
Atletico's shareholders also approved an increase of equity and strategic capital up to an additional 100 million euros ($116 million) to support the club's investments.
