Iraq's new interim government has been sworn in at a ceremony in Baghdad, to begin the task of preparing the country for elections in January next year.
Mr Allawi was named prime minister last week
It will begin taking up its powers at once, after a surprise decision by the Governing Council, formed last July, to dissolve itself with immediate effect.
The changes took place within hours of Ghazi Yawer being named as president.
President Bush praised the new interim government saying it had the "talent" to guide Iraq over the next months.
Both Mr Yawer and interim Prime Minister Iyad Allawi were the favoured candidates of the Iraqi Governing Council.
The swearing-in of the interim administration follows days of wrangling between the council and American officials in Iraq.
KEY CABINET POSTS
Interior minister: Falah al-Naqib
Foreign minister: Hoshiyar Zebari
Defence minister: Hazim al-Shalaan
Finance minister: Adel Abdul Mehdi
The US officials, along with UN envoy Lakhdar Brahimi, preferred veteran Sunni politician Adnan Pachachi to take over the largely ceremonial role of president.
Earlier reports said Mr Pachachi, an ex-Foreign Minister, had been chosen as president but had declined the job, reportedly because he had little backing among his fellow council members.
BBC Middle East analyst Roger Hardy says that in the three-way tussle between the council, the chief US administrator Paul Bremer and the UN special envoy, the council has proved remarkably successful in getting its way.
In the first reaction by a senior US official, National Security Adviser Condoleezza Rice said the formation of an interim Iraqi government was a "positive step for the future of a free Iraq".
Her comments were later echoed by US Secretary of State Colin Powell who said it was "a good day for the Iraqi people" and that President George W Bush's five-point plan for Iraq was now unfolding.
He denied any rift between the IGC and US-led coalition, saying it had not been a case of each side wanting a different candidate.
Mr Powell said the important thing was that the Iraqi people had been allowed to make their own choice and that the US had been gratified to see so many capable candidates vying for the top jobs.
At the swearing-in ceremony, Mr Yawer said his goal was to make Iraq one nation, "without murderers and criminals".
He said he wanted a pluralistic, democratic and federal Iraq that would live in peace and co-operation with its neighbours.
Mr Yawer is a US-educated civil engineer and tribal leader who has recently criticised the way the US has handled security in Iraq.
IRAQ SELF-RULE TIMETABLE
30 June: Handover from Coalition Provisional Authority to interim government
End of Jan 2005: Elections to National Assembly
Autumn 2005: New constitution voted on in referendum
December 2005: Full elections for new government
January 2006: Directly elected government takes office
Mr Allawi for his part said that while he wanted the US occupation of Iraq to end as soon as possible, for now coalition forces would remain in place.
He expressed gratitude for what the coalition forces had done thus far in Iraq, saying "We will need the participation of the multinational forces to help in defeating the enemies of Iraq".
The full handover of power to the Iraqis is scheduled to take place on 30 June, a day which Mr Allawi said would be a major step in creating a new, sovereign Iraq.
BBC News Online world affairs correspondent Paul Reynolds says that the interim government has turned out to be a more political body than the government of technocrats originally proposed by Mr Brahimi.
At least three people are reported to have been killed in the latest blast
This reflects, our correspondent says, a feeling that Iraq needs some leadership at this moment. Some of the government's key figures are from the Governing Council which has exerted its influence in the negotiations.
The dramatic political developments came as a series of blasts were heard in the centre of Baghdad.
Witnesses said a car bomb exploded near the headquarters of the Patriotic Union of Kurdistan Party, close to the Iraqi foreign ministry.
There are conflicting reports about the number of casualties - latest reports say three people have died, and more than 30 were injured, but earlier, at least 10 people were said to have been killed.
Witnesses also said at least four mortars had been fired at the headquarters of the US-led coalition in the so-called Green Zone.
And the US military announced the death of a US soldier from the First Marine Expeditionary Force, who was killed during an operation in Anbar province, western Iraq, on 31st May.