Relations between Qatar and Egypt have been icy since July 2013, when then-Egyptian army chief Abdel-Fattah al-Sisi toppled Morsi after mass unrest against his rule.
Qatar had supported Morsi, who is already in jail along with thousands of Muslim Brotherhood members, many of whom have been sentenced to death on separate charges.
Security sources had said last month that Egypt was investigating Morsi in connection with documents they said were leaked to Qatar and its satellite news channel Al Jazeera.
The Cairo public prosecutor's office said Saturday that its secret investigation had unearthed enough evidence of espionage to charge Morsi in a criminal court.
"The inquiries... exposed humiliating facts and the extent of the largest conspiracy and treason carried out by the terrorist Brotherhood organization against the nation through a network of spies," it said in a lengthy statement.
The statement said Morsi and two of his top secretaries abused their positions to slip documents from Egypt's security agencies to Qatari intelligence and Al Jazeera.
It said some of those documents exposed the location of and weapons held by the Egyptian armed forces and detailed the country's foreign and domestic policies.
The Qatari Foreign Ministry in Doha did not immediately respond to requests for comment on the accusations.
Al Jazeera, which has been banned from Egypt, has denied any bias in reporting events there or any role in aiding the Brotherhood.
It was not immediately possible to obtain a Brotherhood comment as most of the group's leaders are in Egyptian jails.
Sisi, who went on to win a presidential election in May, promised during his campaign that the Muslim Brotherhood would cease to exist under his rule.
Egyptian security forces killed hundreds of Brotherhood supporters during protests against Morsi's ouster and thousands of others have been jailed.
Egypt's oldest Islamist movement, once among Egypt's most formidable political forces, has been branded a terrorist group and its assets have been seized by the state. The Brotherhood formally renounced violence as a means of political change decades ago and has denied any role in more recent bloodshed.
While Sisi has taken the reins of power, Morsi has languished in jail on charges of inciting violence and various other offences.
Egypt has jailed three Al Jazeera journalists for up to 10 years on charges of aiding "a terrorist group" by broadcasting misinformation that harmed national security. Al Jazeera has said the charges are baseless.
RA/SHI