He is expected to be Bayern’s second recent signing from the Dutch champions after Morocco right-back Noussair Mazraoui, 24, joined last month on a free transfer.
“Bayern is a big club. I think you have to win big titles here,” Gravenberch told German daily Bild after landing at Munich airport on Saturday.
“That’s also what I expect. I’m happy to be here in Munich.”
Gravenberch, 20, is set to cost an initial fee of 18.5 million euros ($19.5 million) which could rise by 5.5 million euros in additional payments.
He mainly plays as a central midfielder but is versatile enough to also play a defensive role.
Ajax would also reportedly have a 7.5 percent stake if Bayern sell Gravenberch.
He has played for each level of the Netherlands’ national teams from Under-15 upwards and made 103 appearances for Ajax, including 14 in the Champions League, since his senior debut in 2018.