Egypt's Supreme Electoral Committee (SEC) was expected to announce the final results of this week's referendum a day after clashes between security forces and Islamist protesters killed four people.
Preliminary results indicated that around 97.7 per cent of voters endorsed the new constitution and that the turnout was between 40 to 50 per cent.
The new charter would replace the one approved under Morsi, who was toppled by the military in July following mass protests demanding his ouster.
The referendum is a key step in the political transition plan billed by the military-backed interim government as a path to democracy, even as it presses a fierce crackdown on the Brotherhood.
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The roadmap was announced by army chief Gen Abdel Fattah al-Sisi after Morsi's ouster.
It stated that the constitution would be followed by parliamentary elections and presidential polls.
The new charter, drafted by a liberal-dominated committee appointed by the government, would ban political parties based on religion, give women equal rights and protect the status of minority Christians.
The "yes" vote would also provide a popular mandate for military chief Sisi to run for president in elections later this year.
Sisi has yet to say outright whether he plans to seek the nation's highest office, but his candidacy appears increasingly likely.
Morsi, the first democratically elected president, is being held in jail in Alexandria, facing several criminal charges relating to his time in office. He says they are politically motivated.