Final figures from the elections commission showed the constitution was adopted with 63.8 percent of the vote, giving Islamists their third straight victory at the polls since Hosni Mubarak was toppled in a 2011 revolution.
Mursi's Leftist, liberal, secularist and Christian opponents had taken to the streets to block what they argued was a move to ram through a charter that would dangerously mix politics and religion.
The president argues that the new constitution offers sufficient protection for minorities, and adopting it quickly is necessary to end two years of turmoil and political uncertainty that has wrecked the economy.
Hours before the vote result was announced, the authorities imposed a new ban on travelling in or out of the country with more than $10,000 in foreign currency, a move apparently intended to halt capital flight.
Some Egyptians have begun withdrawing their savings from banks in fear of tougher restrictions.
The "yes" vote paves the way for a parliamentary election in about two months, setting the stage for yet another electoral battle between surging Islamists and their fractious liberal and leftist opponents.
The final result, announced by the election commission, matched - to the last decimal place - an earlier unofficial tally announced by Mursi's Muslim Brotherhood.
The constitution was drawn up by a body largely made up of Mursi's Islamist allies. The results announcement was a disappointment for the opposition which had put pressure on the authorities to recount the result to reflect what they have described as major vote violations.
"We have seriously investigated all the complaints," judge Samir Abu el-Matti of the Supreme Election Committee told a news conference. The final official turnout was 32.9 percent.
Cairo, gripped by often violent protests in the runup to the vote, appeared calm after the announcement and opposition groups have announced no plans for demonstrations to mark the result.
"The results was so odd and no change in the percentage points shows that nothing was done to take our complaints into account," Khaled Dawood, an opposition spokesman, said.
The referendum, held on December 15 and on December 22, has sown deep divisions in the Arab world's most populous nation but Mursi says enacting the new constitution quickly will bring stability and a chance to focus on fixing the economy.
A growing sense of crisis has gripped Egypt's polarised society for weeks. Standard and Poor's cut Egypt's long-term credit rating on Monday (local time).
Hours ahead of the results announcement, Prime Minister Hisham Kandil told the nation of 83 million the government was committed to taking steps to heal the economy.
"The main goals that the government is working towards now is plugging the budget deficit, and working on increasing growth to boost employment rates, curb inflation, and increase the competitiveness of Egyptian exports," he said.
The central bank said on Monday it would take steps to "safeguard" bank deposits, without giving any details. Rumours are rife of what sort of measures are planned.
"I have been hearing that the central bank is going to take over all our bank deposits to pay wages for government employees given the current deteriorating economic situation," said Ayman Osama, father of two young children.
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 jewellery.
"I am not going to put any more money in the bank and neither will many of the people I know," he said.
The referendum is the Islamists' third electoral victory since the fall of Mubarak, following parliamentary and presidential elections, representing a decisive shift in a country at the heart of the Arab world, where Mursi's Muslim Brotherhood was suppressed for generations by military rulers.
However, secularist and liberal opposition members hope they can organise better in time for the next parliamentary vote.
The opposition says the constitution fails to guarantee personal freedoms and rights for women and minorities. The government says the criticism is misplaced.
Hossam El-Din Ali, a 35-year-old newspaper vendor in central Cairo, said he agreed the new constitution would help bring some political stability but like many others he feared the possible economic austerity measures lying ahead.
"People don't want higher prices. People are upset about this," he said. "There is recession, things are not moving. But I am wishing for the best, God willing."