The Brotherhood said about 64 percent of the voters cast a “yes” ballot for the charter over two days of voting. The first round was held on December 15 and a second round took place Saturday. Voter turnout was reported to be only about 32 percent.
If the preliminary outcome is confirmed in the coming days, a parliamentary election is to take place in two months.
The Muslim Brotherhood, the party of Egyptian President Mohamed Morsi, supports the new constitution. However, members of Egypt's liberal, secular and Christian opposition note it will erode civil liberties, because it is based in Sharia law and has no mention of women's rights.
A largely Islamist committee approved the draft constitution last month after ignoring liberal and Christian members.
Late Saturday, Mr. Morsi is reported to have announced the names of 90 new members he has appointed to the upper house of parliament. The list is claimed to include liberals and other non-Islamists as a means to continue dialogue among the factions.
Violent protests and clashes led up the to referendum vote. Several people were killed and many others wounded in Cairo earlier this month.