Egyptian Seif al-Din Mohamed Mostafa, 58, is accused of using a fake suicide belt to seize the Alexandria-to-Cairo flight on March 29 and force it to land in Cyprus.
Cypriot government officials said that a legal process would now begin to send home the 58-year-old, who is in police custody on the island.
"Instructions were given for the relevant procedures to begin," a government official told AFP.
Nicosia is expected to try to fast-track the extradition process which could take several weeks.
The Egyptian state prosecutor's office had asked for him to be handed over under a 1996 bilateral extradition treaty.
Mostafa -- described by authorities as psychologically unstable -- has said he acted out of desperation to see his Cypriot ex-wife and children.
Cypriot prosecutors said last week he faced possible charges of hijacking, kidnapping, reckless and threatening behaviour, and breaches of the anti-terror law.
According to police, Mostafa has given a voluntary statement admitting to the hijacking.
His ex-wife has been quoted by Cypriot media as describing their five years of marriage as a "black period" of her life.
Most of the 55 passengers were quickly released after the plane landed, but some escaped only minutes before the six-hour standoff finished.
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