Turnout was 38.6% of the 53 million eligible voters, the election committee said.
The draft constitution replaces one introduced by Islamist President Mohamed Morsi before he was ousted.
The referendum is being seen as a vote on the legitimacy of Mohamed Morsi’s removal and of the army, which toppled him in July last year.
The vote, which took place on Tuesday and Wednesday but was boycotted by members of the Muslim Brotherhood, the Islamist movement from which Mohamed Morsi comes and which wants to see him returned to office.
Several people died in violence involving Mohamed Morsi’s supporters on the first day of voting.
There were further clashes with the security forces on Friday in which four people died, the Health Ministry said.
Election Commission head Nabil Salib called the vote an “unrivalled success” with “unprecedented turnout”, AP news agency reported.
A constitutional referendum held in 2012 while Mohamed Morsi was in power but boycotted by secularists saw a turnout of 33%, with 64% of voters approving the document.
The new proposed constitution was drafted by a 50-member committee that included only two representatives of Islamist parties.
Critics say the document favors the army at the expense of the people, and fails to deliver on the 2011 revolution that led to the fall of Hosni Mubarak.
Under the draft:
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