About 15 million Iraqis were eligible to vote in the polls, held in 14 of the country's 18 provinces.
More than 14,000 candidates, 4,000 of them women, competed for seats.
Iraq's provincial councils are responsible for nominating the governors who lead the administration, and oversee finance and reconstruction projects. They control a combined budget of $2.4bn.
Speaking to Al Jazeera, Richard Engel, NBC's chief foreign correspondent in Baghdad, said calm prevailed on the streets of Baghdad on Sunday.
"It is not a record turnout that some people had hoped for, but it is a strong turnout," he said.
Elections were held in 14 of total 18 provinces
About 15 million Iraqis were eligible to vote
There were 5 major parties to choose from
More than 14,000 candidates contested the polls
"What was so significant about this is that there was not a single major attack all across Iraq at the many polling stations ... and that, according to Iraqi security services and the Iraqi people, was a significant accomplishment - the most peaceful election the country has had since the fall of Saddam Hussein."
Al Jazeera's Anita McNaught, reporting from Irbil in northern Iraq, said although the voting appeared to have gone very well, Iraqi security forces had intercepted boxes containing fraudulent votes in the Salahuddin province region near the area of Tikrit.
She said voting had been peaceful and "there wasn't an uptick in violence, as people were fearing".
Earlier, Ahmed Chalabi, the head of the Iraqi National Congress, told Al Jazeera: "A society broken by Saddam Hussein and 35-years of single party rule has healed itself very speedily - despite the US invasion and the mistakes committed by the American ocupation.
"We are leaving behind the crimes of Saddam and we are moving towards the next stage.
"Iraq is free now, the American occupation is ended [and] President [Barack] Obama is pulling out the troops faster than was agreed," he said.
"I believe the challenges now are economic and developmental. We are one of the richest countries with one of the poorest people in the world. I hope the election later this year will improve this."
Nuri al-Maliki, the Iraqi prime minister, called the polls "a victory for all the Iraqis", after casting his ballot in the highly fortified Green Zone in Baghdad.
Elections are not taking place in the three autonomous Kurdish provinces, Irbil, Dohuk and Sulaimaniya, until later in the year.
Polls in the oil-rich Kirkuk province, which the Kurds want to incorporate into their region despite fierce opposition by the central government, have also been postponed indefinitely.
The killing of three Sunni Arabs candidates on Thursday, and that of a Shia politician two weeks earlier, had raised fears of violence on election day.
Iraqi and US military commanders had also warned that al-Qaeda posed a threat to the elections, and the US military said it was sending heavy deployments of troops onto the streets during the voting.
Hundreds of women, including teachers and civic workers, were recruited to search female voters after a rise in female suicide bombers last year.
Almost 300,000 local and international observers monitored the elections.
The independent electoral commission said it had received very few complaints about attempts of vote buying, but the issue has become a talking point among Iraqis.