FilGoal.com learned on Wednesday that the emerging Egypt star penned a deal with Zamalek before extending his Ittihad contract, which was due to expire at the end of the season.
Geddo denied that he agreed to join Zamalek but the Cairo club objected to his statement in a steadfast manner.
"The player has officially signed a contract with us," Zamalek football director Ibrahim Hassan told FilGoal.com on Thursday.
"We respect all the clubs, including Ittihad, but we will not give up our rights.
"We opened negotiations with him in January because he had just six months remaining on his deal. We legally acted in an appropriate way.
"We presented our documents to the Egyptian FA and will shortly reveal more details about the matter."
Alexandria-based club Ittihad, who said lately that Geddo was going nowhere because he prolonged his deal with them, are yet to comment on Zamalek's announcement.
Geddo rose to prominence after playing a key role in Egypt's triumphant Nations Cup campaign last month.
He finished as the top scorer with five goals although he did not start any game in the biennial tournament.
The 25-year-old also scored the decisive winner in Egypt's 1-0 final victory over Ghana.
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