According to Egyptian state TV, the articles passed stipulate that Islam is the religion of the state, and the principles of Sharia, or Islamic law, are the "main source of legislation".
The Islamists-dominated Assembly sent the draft to President Mohamed Mursi, who is expected to submit it for public approval in a referendum.
Liberal and leftist members and church representatives withdrew from the Assembly in protest at what they saw as attempts by the body's Islamist majority to force its views through.
The draft is unchanged from the previous Constitution under Hosni Mubarak, who was toppled as president last year in a popular uprising.
The draft also says that Christianity and Judaism will be the "main source of legislation" for Egyptian Christians and Jews.
The Assembly also adopted a new article that al-Azhar mosque and university, authorities on Sunni Muslim jurisprudence, must be consulted on "matters related to sharia".
The president's tenure will be limited to two four-year terms.
The opponents of the draft voiced concern that some clauses - such as the importance of promoting family values - could be used to restrict freedom of speech.
They also said that there was no specific article establishing equality between men and women.
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