The Blues have agreed to a transfer with the Dutch club, which will see the player move for next season.
And the Morocco international's arrival could spell the end for a number of Chelsea players.
It is not believed that Ziyech will be the only major signing of the summer, as the Blues also want a first team centre-forward.
But he is the start of the rebuild of manager Frank Lampard from a transfer perspective, as the club had a ban in the summer and did not sign anyone this winter.
Clearing veterans off the wage bill should help Lampard fund further deals.