The presidency council, made up of President Jalal Talabani and his two deputies, now has to announce a date for the election.
The new law sidesteps a veto that Vice President Tareq al-Hashemi had threatened, and comes just minutes before a midnight deadline for Hashemi to torpedo the law.
Hashemi had vetoed a previous version of the law last month, leading to further negotiations and delaying already late elections.
The law will expand parliament from 275 seats to 325, 310 of which will be allotted to Iraq's 18 provinces, with the remainder reserved for religious minorities and blocs that garnered national support but did not win seats in individual provinces.
It is a revised version of the first draft of the election law, with three additional seats for provinces in northern Iraq's autonomous region of Kurdistan, and one fewer reserved seat.
Kurdish parties expressed concerns that their seat allocations had not risen above the 2005 figures, while predominantly Sunni and Shiite provinces had seen increases, a parliamentary official said, speaking on condition of anonymity.
The official told AFP that UN and US diplomats lobbied MPs over the weekend to reach agreement on the law, which had been debated by lawmakers for more than two months.
No definitive date has yet been set for the election which had originally been scheduled for January 16 but was delayed because of the failure by MPs to agree on the new law.
The United Nations on Wednesday proposed February 27 as the most "feasible" date for parliamentary elections, nearly a month later than the deadline laid down by the constitution.
Samarrai has said the election could be delayed to as late as March.
In principle, the constitution requires that the general election, the second since a US-led invasion ousted dictator Saddam Hussein in 2003, be held by the end of January.
A law was initially passed on November 8 but Hashemi, a Sunni, vetoed it 10 days later, citing a lack of representation for Iraqi exiles, the vast majority of whom are Sunnis.
MPs subsequently passed a second version, which Hashemi threatened to veto, that upped the number of seats for Kurds but reduced that figure for Sunnis, leading to the protracted negotiations that concluded on Sunday evening.
American diplomats had pushed MPs to pass the law, with Washington seeking to avoid delays to the planned pullout of tens of thousands of its troops from Iraq in 2010.
The United States has 115,000 soldiers in Iraq, but that figure will drop markedly next year as all of its combat troops are pulled out before a complete withdrawal by the end of 2011.
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