Iraqi officials say there could be some preliminary results available in a day or two, but a full, official count will take longer.
Estimates put the turnout in the referendum at some 10 million people. That's about 65 percent of the electorate, a turnout that world leaders praised as courageous in view of the ongoing insurgency.
U.S. President George W. Bush called the referendum a critical step.
"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.
Members of Iraq's majority Shi'ite community danced in the streets after voting ended on last night.
A massive security clampdown prevented any serious insurgent attacks on voting day, with only scattered violence reported.
Today several mortar rounds landed in the high-security Green Zone in central Baghdad, which contains diplomatic and military installations, but there's no word on any casualties.
(AFP/Reuters/AP)For RFE/RL's full coverage of Iraq's constitutional referendum, see "Iraq Votes 2005"