According to the Iraqi Independent Election Commission, 78 percent voted "yes" and 21 percent voted "no."
The constitution's fate rested on results from Nineveh, a mixed province of Sunni Arabs, Shi'a, and other groups.
Under Iraqi law, two-thirds of voters in at least three of the country's 18 provinces must reject the charter for it to be defeated outright. Voters in Iraq's other 15 governorates overwhelmingly supported the draft, election officials said.
Farid Ayar of the election commission of Iraq hailed the poll. "The referendum -- whatever its results, whether the 'yes' votes prevailed over the 'no' votes, or vice versa -- is a progressive step aimed at placing Iraq on the track of true democracy in order to build a modern society compatible in its features with the world," he said. "It is also a success for all Iraqis without exception."
Carina Perelli, the head of the UN's electoral assessment mission in Iraq, said the balloting had adhered to the highest standards and should be trusted.
The European Union welcomed the results, but a prominent Sunni Arab official, Salih al-Mutlaq, criticized the referendum as fraudulent.
Supporters say the constitution will help Iraq's democratic transformation. Sunni Arabs say it gives too much power to Kurds and the majority Shi'a.
The result clears the way for Iraq to hold its first national elections for a full, four-year government in December.
(With news agencies)