Independent Election Commission spokesman Adil al-Lami said voter turnout was more than 61 percent nationwide.
Earlier, election commission head Izz al-Din al-Muhammadi told Radio Free Iraq that he was pleased with the participation.
"In all areas, even those that boycotted the [January] election, the reports we have received indicate that turnout is good and participation high in the referendum," al-Muhammadi said. "This, God willing, bodes well for the coming days."
Government spokesman Laith Kubba hailed it as a success, regardless of how people voted.
"Today is a day of national consensus on participation regardless of who will vote 'yes' or 'no.' I think that, as Iraqis, we can be proud of that. This is a first and major step towards saying 'no' to political violence. We are seeing turnout even in areas that until recently have been hot and violence-racked, but they are now taking part and saying 'yes' to the ballot box. All these are favorable signs," Kubba said.
As voting neared its close, there was praise from U.S. President George W. Bush, who said the constitution is a document that protects fundamental freedoms and lays the foundation for a lasting democracy.
"By casting their ballots, the Iraqi people deal a severe blow to the terrorists and send a clear message to the world: Iraqis will decide the future of their country through peaceful elections, not violent insurgency," Bush said.
Security largely held across the country, although several polling stations in Baghdad were attacked and a roadside bomb killed three Iraqi soldiers northeast of the capital .
The constitution will be ratified if more than 50 percent of voters voted "yes," and as long as two-thirds of voters in any three of Iraq's 18 provinces did not vote"no."
Initial results may be announced later tonight although a complete tally is not expected before 17 October at the earliest.
(Radio Free Iraq, news agencies)For RFE/RL's full coverage of Iraq's constitutional referendum, see "Iraq Votes 2005"