Grapel, 27, was arrested in Egypt on accusations he was a spy out to recruit agents and monitor events in the revolt that overthrew President Hosni Mubarak, an ally of both the United States and Israel. Grapel has not faced trial yet.
US Defense Secretary Leon Panetta called on Egypt this month to release Grapel but denied he was involved in direct negotiations over the matter.
"In response to the demands of the families of Egyptian prisoners held in Israel, the cabinet has decided that the Foreign Ministry coordinate with all the concerned security entities to take the necessary steps to return those prisoners to their homeland," cabinet spokesman Mohamed Hegazy said.
"This includes the exchange of the accused Ilan Grapel with those prisoners and taking the necessary legal steps involved."
An Egyptian security source said earlier this week that such a deal was expected. Media reports said more than 80 Egyptian prisoners in Israel would be involved in the exchange.
Grapel's mother said at the time of his arrest that her son, a law student in the United States, was working for Saint Andrew's Refugee Services, a non-governmental organisation, in Cairo.
Grapel emigrated to Israel in 2005 from New York and served in its military in the 2006 Lebanon war.
Over the years, Egypt has arrested a number of people accused of spying for Israel.
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