The two clubs agreed a fee of €40 million ($43.4m), with Gravenberch set to undergo a medical in Liverpool late Thursday or Friday.
Gravenberch, 21, has spent just a single season at Bayern after signing from Ajax Amsterdam last summer on a five-year deal.
The Netherlands international will bolster a Liverpool midfield that has seen the departures of several key players this summer.
After Naby Keita, James Milner and Alex Oxlade-Chamberlain left following the expiration of their contracts, manager Jurgen Klopp also lost Jordan Henderson and Fabinho following their surprise transfers to the cash-rich Saudi Pro League.
The Ajax academy graduate has made 34 appearances for Bayern, but started just three games in the Bundesliga. He has 11 caps for the Netherlands.