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 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.