"I signed a five-year deal with Zamalek, but I am not ready to reveal the details of my contract," the 21-year-old midfielder told FilGoal.com.
It is believed that Shams will receive EGP 1million in compensation for Al-Saied, who plays as a defensive midfielder.
Zamalek beat off competition from ENPPI for the services of the promising midfielder.
Die Foneye interest
Meanwhile, FilGoal.com has learnt that Zamalek are in talks with ENPPI over striker Vincent Die Foneye.
Zamalek enquiry for the Ivorian hitman was acknowledged by their Cairo rivals, who are asking for $1.5million in return.
The White Knights have already signed striker Ahmed Gaafar from Telecom Egypt last week.
Die Foneye scored seven league goals last season as ENPPI finished fifth.