Liverpool have been holding talks with Bayern Munich in an attempt to agree a fee for the Dutch midfielder, who wants the move.
They have now managed to find common ground with the Bavarians and will pay a fixed fee of €40m to sign the midfielder.
Gravenberch will now travel to Liverpool this evening and then the Reds will put him through his medical paces.
If he comes through the medical checks without an issue then he will put pen to paper to a long term deal at Anfield.
Gravenberch hands Jurgen Klopp the extra midfielder he has been looking for.
Bayern Munich are expected to move to sign a replacement for Gravenberch and are keen on Fulham’s Joao Palhinha.
Gravenberch started just three league games for Bayern Munich over the course last season as he struggled to make an impact.