"It is an accomplishment for all Iraqis," said commission spokesman Farid Ayyar in announcing the results 10 days after the landmark referendum on a charter that lays down a democratic future for the post-Saddam Hussein Iraq.
"The results are precise and honest," Ayyar insisted.
Nation-wide, 78 percent of Iraqis voted for the constitution, the commission said, while opponents failed to muster a two-thirds majority against in at least three of Iraq's 18 provinces which would have meant its rejection.
In the mainly Sunni northern province of Nineveh which held the key to a possible veto, after an overwhelming "no" vote in two other provinces, 55.08 percent voted no.
"It's a civilised step that puts Iraq on the path to democracy, to rebuilding our new Iraq," added Ayyar.
The United States and Britain were among the first to congratulate Iraq on the referendum result.
But 2.1 million of Iraq's 15.5 million voters nonetheless opposed the constitution, largely a result of fears among Sunni Arabs that it will place too much power in the hands of regions and lead to a break-up of Iraq.
"The referendum led to a split instead of a union," said political science professor Hasan Bazaz.