Final figures from the elections commission showed the constitution passed with 63.8 percent of the vote in the referendum held over the last two Saturdays, Reuters reported. But the turnout was only a third, the lowest in any vote since the revolution, Al Jazeera noted.
"We have seriously investigated all the complaints," Samir Abu al-Matti, of the Supreme Election Committee, told a news conference.
Morsi said the text - Egypt's first constitution since dictator Hosni Mubarak's fall almost two years ago - offers enough protection for minorities, and adopting it quickly is necessary to end two years of turmoil and political uncertainty that has wrecked the economy.
Mohammed Badie, leader of the Muslim Brotherhood, offered congratulations on the passing of the constitution and said Egyptians continue to "teach" the world, CBS reported.
"Let's all begin to build the renaissance of our country with free will, good intentions and strong determination, men, women, Muslims and Christians," Badie said on his Twitter account.
"We need a better constitution," said Khaled Dawood, a spokesman for the opposition National Salvation Front, which tried in vain to stop the referendum. "It does not represent all Egyptians."
The U.S. reaction came from State Department spokesman Patrick Ventrell.
"President Morsi, as the democratically elected leader of Egypt, has a special responsibility to move forward in a way that recognizes the urgent need to bridge divisions," he said.
“We hope those Egyptians disappointed by the result will seek more and deeper engagement. We look to those who welcome the result to engage in good faith. And we hope all sides will re-commit themselves to condemn and prevent violence."
Immediately after the announcement, a small group of protesters set tires on fire and blocked traffic near Tahrir Square, the cradle of Egypt's uprising, but there were no immediate signs of violence or major demonstrations, Reuters reported.
In a sign that weeks of unrest have taken a further toll on the economy, the government imposed new restrictions on foreign currency to prevent capital flight. Leaving or entering with more than $10,000 cash is now banned.
The ban on traveling with more than $10,000 in cash followed a pledge by the central bank to take unspecified measures to protect Egyptian banks. Some Egyptians have begun withdrawing their savings in fear of more restrictions.
"I am not going to put any more money in the bank and neither will many of the people I know," Ayman Osama, father of two young children, told Reuters.
He said he had taken out the equivalent of about $16,000 from his account this week and planned to withdraw more, adding that he had also told his wife to buy more gold jewelry.
Morsi is now expected to call parliamentary elections within two months. In the meantime, all legislative power will now be transferred from the presidency to the upper house of parliament.
All decrees issued issued since the revolution of February 2011, meanwhile, now stand null and void. These include both those passed by Morsi and those passed by the supreme military council, which ruled Egypt for 16 months after the revolution.
The Supreme Court will also be reshuffled, with its members decreasing from 19 to 10. Morsi is expected to announce the name of the new head of the court within the next few days, Al Jazeera reported.