"The Egyptian people continue their march towards finalizing the construction of a democratic modern state, after turning the page on oppression," a statement released by the Muslim Brotherhood's Freedom and Justice party said.
Preliminary results of Saturday's polling show 64 percent voted in favor of the constitution and 36 percent rejecting it, al-Masry al-Youm said Sunday.
After two rounds of voting, official results are not expected until Monday, the BBC said, noting if the constitution passes, parliamentary elections must be held within three months.
Public support of the constitution will give a boost to Islamists who believe the new constitution will pave the way for a smooth and swift transition to democracy under President Mohamed Morsi, Ahram Online said.
Hours before voting ended Saturday, Vice President Mahmoud Mekki announced his resignation, saying politics does not suit his professional background, Egyptian media reports said. In the past month, some 17 of Morsi's top advisers have resigned, the BBC said.
Meanwhile, Morsi's presidential spokesman Yasser Ali said the president had appointed 90 members to the Shura Council the upper house of Parliament, including senior Muslim Brotherhood leaders, al-Masry al-Youm said.
On Nov. 22, Morsi issued a decree granting himself new powers, stripping the judiciary of the ability to question his decisions. His decision caused a major public outcry and led to violent demonstrations throughout Egypt between Morsi's supporters and opponents. Morsi then revoked the initial decree but refused to back down on the draft constitution, the BBC said.