Former exile Iyad Allawi has been chosen to head an interim Iraqi government after sovereignty is handed back on 30 June.
Allawi spent years in exile under Saddam Hussein
Mr Allawi - a Shia Muslim - was endorsed unanimously by the Governing Council, member Mahmoud Othman said.
A United Nations spokesman has said UN envoy Lakhdar Brahimi - who is charged with choosing the interim government - "respects" the nomination.
The cabinet will govern Iraq until direct elections scheduled for 2005.
Mr Allawi, a British-educated neurologist, left Iraq after turning against Saddam Hussein in the 1970s.
Chief US administrator in Iraq Paul Bremer attended Friday's session of the interim Iraqi Governing Council (IGC) and congratulated Mr Allawi on his nomination, according to an aide to the IGC quoted by the AP news agency.
But the BBC's Jon Leyne at the UN in New York says Mr Allawi was evidently not Mr Brahimi's first choice and the UN's response has been most confused.
The UN says that Mr Brahimi was not even in the room when Mr Allawi was named by the IGC.
Born 1945 to Shia merchant family
Trained in UK as a neurologist
Former Baathist, but fell out with Saddam Hussein
Co-founder of Iraqi National Accord
Initially a UN spokesman in the region said Mr Brahimi welcomed the choice.
But later in New York, chief UN spokesman Fred Eckhard said: "Mr Brahimi respects the decision and is prepared to work with this person on the selection of the other posts in this interim government".
Mr Eckhard insisted there was no discrepancy between the two statements - but he conceded that the decision had not been announced in the way expected.
A senior official at the UK Foreign Office meanwhile said the IGC had "jumped the gun" by announcing Mr Allawi as their choice.
But Mr Brahimi had "anyway been coming to the conclusion that Allawi was the right person," the official added.
In 1978, while living in London, Mr Allawi survived an assassination allegedly ordered by Saddam Hussein.
He later became a founding member of the Iraqi National Accord, a group of exiles backed by US and British intelligence that included many former military officers opposed to the Baghdad regime.
BBC Middle East analyst Roger Hardy says Mr Brahimi had originally hoped to form a government of technocrats - people not associated with the main political parties which dominate the Governing Council.
But leading Shia members of the council - including Mr Allawi - resisted what they saw as Mr Brahimi's attempts to bypass them, our correspondent says.
They are reported to have joined forces to oppose the appointment of respected scientist Hussein Shahristani as prime minister - and insisted that the top job should go to one of their own.
Mr Brahimi is engaged in consultations with Iraqi politicians to select a 30-strong team - which will also include a president, two vice-presidents and 26 ministers.
It will formally become the sovereign government of Iraq when the Coalition Provisional Authority (CPA) is dissolved on 30 June.
Under a US-UK plan currently being discussed by the UN Security Council, a US-led multinational force is due to remain in the country.
A new constitution is to be drawn up and put to a referendum in 2005.
Full elections are expected at the end of 2005.