Thousands continue Egypt protests
But Mr Morsi needs the cooperation of judges to oversee the vote, and many have been angered by a decree from Mursi they said undermined the judiciary. Some judges are on strike.
The assembly concluded the vote after a 19-hour session, faster than many expected, approving all 234 articles of the draft, covering presidential powers, the status of Islam, the military's role and human rights.
It introduces a presidential term limit of eight years - Mubarak served for 30. It also bring in a degree of civilian oversight over the military - though not enough for critics.
An Egyptian official said Mr Morsi was expected to approve the document tomorrow and then has 15 days to hold a referendum.
"This is a revolutionary constitution," said Hossam el-Gheriyani, head of the assembly, urging members to campaign for the new constitution across Egypt, after the all-night session.
Critics argue it is an attempt to rush through a draft they say has been hijacked by the Muslim Brotherhood, which backed Mr Morsi for president in a June election, and its Islamist allies.
Two people have been killed and hundreds injured in protests since the decree was announced on November 22nd, deepening the divide between the newly empowered Islamists and their critics.
Seeking to placate opponents, Mr Morsi welcomed criticism but said there was no place for violence. "I am very happy that Egypt has real political opposition," he told state television.
He said Egypt needed to attract investors and tourists. The crisis threatens to derail a fragile economic recovery after two years of turmoil. Egypt is waiting for the International Monetary Fund to finalise a $4.8 billion loan to help it out.
An alliance of opposition groups pledged to keep up protests and said broader civil disobedience was possible to fight what it described as an attempt to "kidnap Egypt from its people".
Several independent newspapers said they would not publish on Tuesday in protest. One of the papers also said three private satellite channels would halt broadcasts on Wednesday.
The draft injects new Islamic references into Egypt's system of government but keeps in place an article defining "the principles of sharia" as the main source of legislation - the same phrase found in the previous constitution.
The president can declare war with parliament's approval, but only after consulting a national defence council with a heavy military and security membership. That was not in the old constitution, used when Egypt was ruled by ex-military men.
Critics highlighted other flaws, such as articles pertaining to the rights of women and freedom of speech.
A new parliamentary election cannot be held until a new constitution is passed. Egypt has been without an elected legislature since a court order the dissolution of the Islamist-dominated lower house in June.
Separately, it emerged a top aide to Mr Morsi, who quit when the leader issued the decree expanding his powers, has joined the country's biggest opposition movement.
Samir Morkos was Mr Morsi's adviser on the transition to democracy and the only Christian in the Islamist leader's team.
He is one of at least two presidential advisers to have stepped down since the November 22nd declaration.