Zabarnyi, 22, will join PSG on a five-year contract worth around €67 million. The deal will keep him at the Parc des Princes until 2030.
After losing Zabarnyi, Bournemouth have also seen another young centre-back, Dean Huijsen, leave the club earlier in the summer.
Bournemouth's coach, Andoni Iraola, is already looking for a replacement. The club is reportedly interested in signing Bafode Diakite from Lille, a defender who was previously valued at £35 million.
Bournemouth previously considered signing Diakite but decided against it. Now, they are willing to re-enter negotiations to bring him to the club.