Hasselbaink thinks the pair will need at least 'six months' to adjust to the rigours of Premier League football.
"We know he's a talented player. We know what he can do. And Chelsea need a player that can score goals.
"But, we also need to give him the time. If you look at [Arsenal star Pierre-Emerick] Aubameyang when he came, he needed six months. So, give him those six months as well."
On Ziyech, Hasselbaink added: "He is very creative, has an excellent left foot, is very good at set pieces and I expect a lot of assists from him.
"He's got that aura around him in that he wants the ball. He wants that responsibility, he's not afraid to score goals.
"Physically, he'll possibly have a problem in the beginning, so he has to be smarter with his physical ability.
"But he is a silky, beautiful player and something that Chelsea don't have – a midfielder with a left foot who can bring something different."