The alliance took 128 of the 275 seats - 10 short of an outright majority. Kurdish parties have 53 seats and the main Sunni Arab bloc 44.
A number of Sunni politicians have alleged fraud, and international observers criticised irregularities.
United Iraqi Alliance 10 seats short of a majority Kurdistan Alliance again likely coalition partner Sunni Arabs gain much greater representation Secular alliances win fewer seats Former PM Iyad Allawi's bloc loses half its seats Deputy PM Ahmed Chalabi's alliance wins no seats |
Those who do not accept the results will have two days to appeal before they are certified as definitive.
Security measures were tightened in Baghdad and three Sunni Arab-dominated provinces amid fears of increased insurgent violence around the time of Friday's announcement.
There were reports of a dawn operation by US and Iraqi troops against insurgents in Baghdad's al-Doura district. Witnesses reported loud explosions and bursts of gunfire.
And a roadside bomb attack, apparently targeting a US convoy, killed at least two civilians and injured several others in the city centre.
On Thursday, 15 people were killed in a double bombing in Baghdad.
In the first attack, a suicide bomber walked into a cafe and blew himself up. Moments later a car bomb exploded near a passing police patrol.
Talk of unity
The final result of the 15 December poll was announced just after 1500 local time (1200 GMT).
IRAQ ELECTION FACTS 275-seat Council of Representatives will have four-year term 18 provinces are taken as separate constituencies 230 seats allocated according to population 45 seats distributed to parties whose ethnic, religious or political support is spread over more than one province 15 million eligible voters One third of candidates in each party must be women |
The UIA's 128 seats was down from its total of 146 in the old transitional parliament elected last January.
The main Kurdish alliance also lost ground, down from 75 to 53, as a smaller rival group gained five seats.
Sunni Arabs increased their representation - a boycott of the January 2005 elections left them with just 17 seats in the old chamber.
The BBC's Jonny Dymond in Baghdad says there is much talk of a coalition of national unity comprising Shia, Sunni Arab and Kurdish blocs, but negotiations could take weeks or even months.
It is hoped that such a coalition will draw the sting from the insurgency, he says.
But one senior Shia politician has already expressed his doubts about that, and Iraq has, over the past three years, seen many false dawns.
Some 2,000 complaints of fraud, violence and intimidation have been noted since the election.
Allegations levelled at the conduct of the election include:
The observers did not reach any final judgement was made on whether the poll was free and fair.