Fahmy's surrender of his Egyptian passport is a necessary first step for him to be released and deported as a foreign national under a decree issued by President Abdel Fattah al-Sisi in November. He also has Canadian citizenship.
The news came after Canadian Foreign Minister John Baird said that Fahmy's release was "imminent" following the freeing of Greste on Sunday.
The two men were arrested in December 2013 along with Egyptian producer Baher Mohamed, and later sentenced to up to 10 years in prison on charges of aiding the blacklisted Muslim Brotherhood.
"He signed the papers more than a week ago" giving up his Egyptian citizenship, a relative of Fahmy told AFP on condition of anonymity.
"It was very hard for him because he is a proud Egyptian who comes from a family of military servicemen."
An Egyptian official following the case told AFP: "The final legal procedures for his deportation are being completed."
He said Fahmy's renunciation of citizenship had already been finalised.
Egyptian police arrested the three journalists at the peak of a diplomatic row between Cairo and Qatar, which owns Al-Jazeera.
The broadcaster had been critical of the deadly crackdown on Morsi's Muslim Brotherhood following the Islamist leader's overthrow.
Qatar has since moved to mend ties with Egypt, and Al-Jazeera has closed its Arabic-language Egyptian affiliate which backed the Brotherhood.
Last month, the three men's convictions were overturned by an appeal court which ordered a retrial but kept them in custody.