The conservative Shiite United Iraqi Alliance won 128 of parliament's 275 seats, the electoral commission said, almost five weeks after Iraqis went to the polls on December 15.
Their allies in the current government, the Kurdish Alliance, won 53 seats.
That left the Shiites and Kurds just three seats short of the two-thirds majority needed to elect a president and push through constitutional reforms.
They are expected to call on at least one of the Sunni Arab parties, to join them in setting up a government of national unity.
Dissatisfaction
Members of the Shiite alliance, however, expressed dissatisfaction at the distribution of the seats, saying their coalition should have been awarded at least eight more seats.
"We will present our objections on the distribution of the seats by the commission, which was not done according to the election law," said Jawad al-Maliki, deputy leader of Prime Minister Ibrahim Jaafari's Dawa party.
"The commission took seats from the bigger parties and gave them to the smaller ones," he said.
His concerns were echoed by Ammar al Hakim of the Supreme Council for the Islamic Revolution in Iraq, the other major Shiite party, who nonetheless acknowledged that the outcome was good for the Alliance.
"The results of the election are a major advancement and a great victory for the Alliance and the will of the Iraqi people," he said.
The Sunni-based National Concord Front, meanwhile, won 44 seats and another Sunni-based party, the National Dialogue Front, won 11 seats.
Sunnis only had 17 seats in the outgoing transitional parliament because of the community's decision to boycott the January 2005 elections.
Even so, the National Concord Front's Saleh al-Mutlak said the results only "confirmed the previous fraud".
The outcome of the election is seen as a crucial milestone in rebuilding Iraq, with hopes pinned on encouraging the disenchanted Sunni community to play a full role in political life and thereby dampen the raging insurgency.
A team of foreign experts probing the poll had said the election was marked by some fraud, but not on a scale that would call into question the final results.
Security
Authorities had tightened security ahead of the release of the results, sealing off three predominantly Sunni Arab provinces to ward off possible rebel attacks.
Iraqi State television said the provinces of Diyala, Salaheddin and Anbar, frequent sites of insurgent attacks, have been sealed off for 48 hours.
Meanwhile, the US military reported a number of joint US-Iraqi operations throughout Baghdad, but would not give details.
Iraqi security sources reported explosions and said Iraqi police commandos were involved in an operation.
The city was also rocked by a massive bomb explosion in the centre of town targeting a passing US military convoy. Two civilians were killed, but the convoy was unharmed, a security official said.
Also in southern Baghdad, a policeman and civilian were shot dead, while police discovered six corpses north of the city.
Kidnappings
Adnan al-Dulaimi, leader of the Sunni Iraqi People's Conference, called for the release of kidnapped US journalist Jill Carroll, who had been trying to interview him when she was kidnapped on January 7.
Meanwhile the families of two Kenyan telecommunications engineers kidnapped this week issued their own appeal, urging their kidnappers to show mercy to men who were simply trying to earn a living.
The two engineers work for the local mobile telephone service company and were kidnapped in an attack on a company convoy that left 10 people
dead.