Some 64 per cent of voters backed the charter over the two rounds of polling, state-run media reported. The final results of the referendum, however, are not expected until tomorrow.
With this, the grouping of Islamists and ultra-radical Salafists, who have won every election since the ouster of long-time ruler Hosni Mubarak in Feb 2011, appeared to have once again outmuscled the largely secular opposition, which claims abuses in voting.
An official of the Brotherhood's political wing Freedom and Justice Party claimed over 71 per cent of the voters cast a "Yes" ballot for the charter yesterday in second and final round of voting.
"According to our calculations, the final result of the second round is 71 per cent voting 'Yes' and the overall result (of the two rounds) is 63.8 per cent," he said.
The "Yes" vote won in the first phase on Dec 15 by a relatively narrow 56.5 per cent. The draft constitution has caused serious divisions in Egypt as it was drafted by an Islamist-dominated assembly from which representatives of the church and liberals withdrew.
The second round of voting yesterday in 17 governorates which hold half of Egypt's electorate held amid allegations of irregularities. Ten governorates voted during the first phase.
The opposition said violations like polling stations opening late and Islamists seeking to influence voters took place in the second round of referendum.
Egypt's Constituent Assembly on Nov 30 in a marathon session approved the draft constitution imposing Islamic values, a move opposed by Liberals as an attempt to restrict freedom of speech and religion in the country.
The articles passed, stipulated that Islam is the religion of the state, and the principles of Sharia, or Islamic law, are the "main source of legislation".
A number of rights groups and opposition parties had filed complaints of violations during the two-round of the vote. They complained that at several places a vote was held without a judge overseeing it and at several places judges were replaced by employees.
Egypt's Justice Ministry had ordered an investigation into the allegations after the first round of voting. Many judges had also boycotted overseeing the referendum, in protest against Mursi's action of "abduction" of the Supreme Constitutional Court.
Eight were killed in deadly clashes between supporters and opponents of Mursi in front of the presidential palace earlier this month. Regular clashes also took place in a handful of governorates, including second largest city Alexandria.