After preliminary results were tallied, president Mohamed Morsi's Muslim Brotherhood and the official Al-Ahram newspaper both reported that about 64 per cent of votes cast were in favour of the new charter.
The early results are based on reports from returning officials from the vast majority of stations over the two rounds, which were held a week apart. The election committee will announce the final results within two days.
An official from Egypt's main opposition group, which campaigned against the constitution, saying it would deepen divisions in Egypt, also said its unofficial count indicated the document was approved.
The first round of voting was held on held on December 15 and a second round was staged on Saturday, with roughly half Egypt's 51 million eligible voters covered in each round.
Turnout over both rounds was around 32 per cent, according to the Muslim Brotherhood.
"According to our calculations, the final result of the second round is 71 per cent voting 'yes' and the overall result is 63.8 per cent," a Brotherhood official, who was in an operations room monitoring the vote, told Reuters.
Murad Ali, a senior official in the Muslim Brotherhood's Freedom and Justice Party, confirmed the numbers.
The Brotherhood and its party, as well as members of the opposition, had representatives monitoring polling stations and the vote count across the country.
The opposition said voting in both rounds was marred by abuses.
"We can tell from the results so far that it will be a 'yes' vote," an official from the National Salvation Front said.
"They (Islamists) are ruling the country, running the vote and influencing the people, so what else could we expect."
Mr Morsi's vice president, Mahmud Mekki, whose post is not mentioned in the new charter, announced Saturday that he was resigning.
"Political work does not suit my professional character," he said in a statement, referring to his past as a respected judge.