Toth moves to the Cherries for €15m with another €3.5m due in bonuses. Ferenvaros hold a 10 per cent sell-on clause as part of the agreement.
The 20 year-old has signed a deal with Bournemouth to 2031.
"When I knew AFC Bournemouth were first interested in me, I was excited and happy because this is a good club in the Premier League, the best league in the world and the strongest league," said Hungary international Toth.
"The whole club, the whole structure is great."
Bournemouth chief Tiago Pinto said: "He has come from a club that is used to competing at the highest level in Hungary, while also featuring in Europe.
"So we're excited about what he can bring to us in Bournemouth as he continues to develop further under the coaching of Andoni (Iraola)."