If adopted, the charter will be put to a popular referendum early next year in the first milestone of the military-installed government's transition roadmap, to be followed by presidential and parliamentary elections in mid-2014.
Voting on the 247 articles began with 48 members of the 50-member panel in attendance, and was expected to continue tomorrow, said Amr Mussa, the head of the panel and former foreign minister under Hosni Mubarak, who was toppled by a pro-democracy uprising in 2011.
After the army ousted Morsi in July, Egypt's interim rulers suspended the 2012 constitution, which had been hastily drafted during his year in power by a panel dominated by Morsi's Islamist allies.
The roadmap stipulates that a referendum on the constitution be held by the end of the year, but officials have said it is now expected in the second half of January.
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But it includes just two Islamists, neither of whom is from Morsi's Muslim Brotherhood, which won a series of polls following Mubarak's ouster but has in recent months been the target of a sweeping crackdown that has seen more than 1,000 people killed.
Mussa told reporters earlier that the panel "reached an agreement on the entire constitution which has been extensively revised" from the one adopted under Morsi.
But rights groups and activists criticised the draft, particularly Article 203, which would allow military trials of civilians accused of "direct attacks" on the armed forces, a provision they fear could be applied to protesters, journalists and dissidents.