Leaders called for the vote to be held before Jan. 31 of next year.
The polls were scheduled for Oct. 1, but an agreement had been bogged down in a complex dispute between Arabs, Kurds and ethnic Turkmen over power sharing in the oil-rich northern city of Kirkuk, which Kurds seek to incorporate into their semiautonomous region.
Kurds believe that they have superior numbers in Kirkuk and consider it their ancient capital. Kirkuk's Arabs and Turkmen want the city to be under central government authority.
The new law requires the committee to recommend separate legislation on Kirkuk. It also banned the use of religious authorities, mosques and government institutions by political parties as part of their campaigning.
While the measure still needs to be approved by the three-member presidential panel, led by President Jalal Talabani who vetoed the last attempt Parliament made to push a measure through, Kurdish legislators agreed to the latest proposal, suggesting presidential approval could be more likely.
The move came the same day as 22 Iraqi policemen and members of a so-called awakening council were gunned down in northeast Baghdad, the U.S. military said.
But even with the day's violence, the U.S. military has reported that overall violence in Iraq has gone down by 80 percent since last year. But until now, Iraqi politicians had failed to take advantage of the lull and pass formative power-sharing laws, frustrating U.S. officials.
The agreement to the Kirkuk law was reached only after Shiite, Sunni, Kurdish and Turkomen lawmakers adopted a U.N. compromise that allowed a separate review process to oversee disputes regarding Kirkuk so that elections in the rest of Iraq could go ahead unimpeded.
Kurdish lawmaker Khalid Shewani said that he was confident that the committee would work in accordance with the Iraqi constitution.
"We succeeded with this committee to resolve a question that had been complicated for some four months," he told the AP. "Every side had fears but these fears have disappeared after the inclusion of legal guarantees."
"We thank God that we reached this agreement," he added.
U.N. envoy Staffan di Mistura, who has been involved in the negotiations between the political groups, told the AP that preparations for the final approval vote would start immediately.
"Today is an important day for Iraq and democracy as the Parliament found a compromise over election law," he told the AP. "This will help Iraq and Iraqis to express their opinions by voting for their candidates in the provinces."
Parliamentary speaker Mahmoud al-Mashhadani, a Sunni, said the law's passage was tangible proof that Iraq's divided and often fractured ethnic and religious groups could work together.
"In the past, Kirkuk was the mother of all troubles, but today it has become the symbol of Iraqi unity," he said.
In Washington, State Department spokesman Robert Wood extended his congratulations to the Iraqi government for passing the law.
"We think this is a positive sign, and it certainly shows a maturing Iraqi democracy," he said. "And we hope that there will be provincial elections held as soon as possible, certainly before the end of the year."
Both U.S. and Iraqi officials believe that elections are a crucial step to forging peace in a country that is still rife with political and religious conflict. In the upcoming election, which a senior election official said could be held four to five months after the law is passed, voters will choose provincial councils in 14 provinces. These councils, at a local level, hold considerable power.