The tally, released also showed that turnout in the two-day referendum was at least modestly higher than a 2012 constitutional ballot held during the rule of deposed president Mohammed Morsi.
An unofficial tally from 25 of Egypt's 27 governorates showed that 97 per cent of voters said yes to the new constitution, with less than one per cent voting no. The remaining ballots were spoiled or otherwise invalid, Al Jazeera reported.
Galal Mustafa Saeed, the governor of Cairo, said he expected turnout in the city to top 40 per cent.
Official media hailed the outcome as an "unprecedented majority".
"Egyptians inaugurate a new history for the region," the state-run Al-Ahram newspaper said.
Colonel Ahmed Ali, the army spokesman, was quoted by the state-run MENA news agency as saying, the result "confirms that Egyptians are the first free population in recorded history."
Although there there were no reports of violence yesterday, at least 11 people were killed in clashes across the country on Tuesday, and a bomb damaged a courthouse in Cairo's Imbaba neighbourhood two hours before polls opened.
The new constitution, like its predecessor, allows the military to prosecute civilians for attacks on army personnel or institutions.
Official results from the two-day referendum are expected to be out by Saturday.
Government sources said interim President Adly Mansour will then issue a decree "within days" to schedule presidential and parliamentary elections, both planned for the first half of this year.
