Iraq's President Jalal Talabani has asked Shia politician Jawad al-Maliki to form the country's next government.
Mr Maliki's nomination could clear a major political stumbling block
The move follows months of political deadlock and has raised hopes of an end to sectarian divisions that have threatened to drag Iraq into civil war.
The dominant Shia bloc picked Mr Maliki as its nominee after the current premier, Ibrahim al-Jaafari, bowed out.
US President George W Bush said the "historic achievement by determined Iraqis will make America more secure".
He offered his congratulations to the Iraqi people and said the day was a milestone on Iraq's path to democracy.
President Bush also hinted that the agreement on Iraq's new leaders could pave the way to the start of an American withdrawal.
"The new Iraqi government will assume greater responsibility for their nation's security," he said.
Now that Mr Maliki has been endorsed as prime minister, he has 30 days to form a government.
Parliament must then approve each member of his cabinet by a majority vote.
BBC correspondent Jim Muir in Baghdad says Mr Maliki will seek to form a national unity government including Shias, Sunnis, Kurds and secular politicians.
But he added that there would be strong competition among the various movements for key posts such as the interior, defence, foreign and oil ministries.
Deputy leader of the Daawa, Iraq's oldest Shia party
Served on de-Baathification committee
Served on committee drafting Iraq's constitution
Deputy speaker of the interim National Assembly
Fled Iraq for Syria in 1980s and returned after invasion
The government faces the challenge of dealing with the insurgency and reversing the trend towards sectarian strife that has increased in recent months, our correspondent says.
In his first policy speech after being asked to form a government, Mr Maliki said Iraq's militia groups must merge with the country's security forces, the Reuters news agency reported.
"Arms should be in the hands of the government. There is a law that calls for the merging of militias with the armed forces," Mr Maliki was quoted as saying.
Sentenced to death by Saddam Hussein for belonging to the Shia Daawa Party, Mr Maliki fled Iraq in 1980 and took refuge in Syria.
He returned after the US-led invasion and was a top negotiator for the Shia bloc in the drafting of Iraq's new constitution.
Mr Talabani (left) asked Mr Maliki to form Iraq's next government
Correspondents say the tough-talking politician was initially considered an unlikely candidate for prime minister, partly because of his proximity to Mr Jaafari.
However, Sunni politicians indicated they would not oppose Mr Maliki.
In Saturday's parliamentary session, MPs elected President Talabani, a Kurd, to a second term in office.
They also gave the post of parliament speaker to Mahmoud al-Mashhadani, a Sunni Arab.
They picked Khalid al-Attiyah, a Shia politician, and Aref Tayfour, a Kurd, to be his deputies.
Attempts by Mr Jaafari to remain as prime minister had raised sharp opposition from Sunnis, Kurds and secular groups.
The impasse had lasted since Iraq held elections in December.
In the meantime, the security situation has worsened and tensions between ethnic and religious communities have grown stronger.
In violence on Saturday:
- Five American soldiers were killed in an explosion south of Baghdad, the US military said
- Two Iraqis died after suspected insurgents set off two bombs in a market in the town of Muqdadiyah, north of Baghdad, the AP news agency reported
- At least 10 bullet-ridden bodies were found in and around Baghdad, some showing signs of torture
US and Iraqi officials are hoping that a national unity government representing Shias, Sunnis and Kurds will be able to quell the Sunni-led insurgency and stem violence between Shias and Sunnis.
If it succeeds, it could help the US begin bringing home its 133,000 troops stationed in Iraq.