The Cairo giants were close to landing Gennesh in January but backed out of the deal following a financial disagreement with his club.
The move fell through when lower division outfit Olympic put an EGP two-million price tag on the keeper's head.
Both sides agreed a new transfer fee on Saturday.
"We have reached a final agreement to acquire the player for EGP 1.5 million and the deal will be wrapped up on Wednesday," Zamalek's marketing director Ashraf Sobhi told FilGoal.com.
"Olympic will receive a down payment of EGP 500,000 and the rest of the money will be paid on three installments."
Zamalek have been on the lookout for a new goalkeeper to play second fiddle to number one Abdul-Wahed Al-Sayed since the departure of Essam Al-Hadari to Merreikh.
The 11-time Egyptian champions signed Palestine goalie Ramzi Saleh in the winter but declared his contract null and void in no time.