The UN Security Council has voted unanimously in favour of a revised US text setting out Iraq's political future.
The US-led coalition will now be able to get on with Iraq's reconstruction
The resolution preserves the dominant role for the US-led administration, but calls upon it to transfer sovereignty and government back to the Iraqi people "as soon as practicable".
The outcome of the vote, after weeks of wrangling, will be hailed by some as a victory for American diplomacy, says the BBC's Greg Barrow at the UN.
An announcement shortly before the vote confirmed France, Germany and Russia - leading critics of the US-led war on Iraq - would back the amended text, ending speculation they might abstain altogether.
But continuing concerns about the text mean they will not contribute troops or funds to the reconstruction effort.
However, US Defence Secretary Donald Rumsfeld said he believed the resolution would have a favourable effect on some countries that may be considering sending troops to Iraq.
The BBC's Nick Childs says the Pentagon will need to know soon what extra foreign forces it may be able to count on as it hopes that they could replace the US Army's 101st Airborne Division, which is due to leave Iraq in February or March.
If foreign troops are not forthcoming, the US military planners will have to switch to a back-up plan involving new American forces amid growing concerns about troops' morale, our correspondent says.
The resolution was also backed by Syria, representing the Arab world on the Security Council.
UN Secretary General Kofi Annan welcomed the vote, saying the Security Council's common objective was to restore sovereignty to Iraq as quickly as possible.
US Secretary of State Colin Powell said the mutual goal was to help the Iraqi people.
He said he hoped the new resolution would lead to more foreign troops and money being offered to assist in the rebuilding of Iraq, although he indicated he did not expect any major financial contribution from France, Germany and Russia.
The resolution is a compromise but "there are more pluses than minuses", Russia's UN ambassador, Sergei Lavrov, told the Security Council after the vote.
France's UN Ambassador Jean-Marc de La Sabliere said France wanted to make unity in the council "a priority".
The shift began on Wednesday and was confirmed after the leaders of France, Germany and Russia discussed the US text and agreed that it went just far enough to win their votes.
The three dissenters had been pushing Washington for concessions on the text which is aimed at winning broad international backing for the reconstruction of Iraq.
The vote was delayed from Wednesday after Russia insisted on the last-minute discussions with its allies.
China - another veto-wielding member of the council - had also been unenthusiastic about the US resolution, which was proposed with the support of the UK, Spain and Cameroon.
But Foreign Minister Li Zhaoxing said on Thursday that the amendments made the text more acceptable.
No big changes
The broad shape of the resolution that was put to the vote has not changed dramatically.
The resolution confirms that for the time being the Coalition Provisional Authority will remain the over-arching power in Iraq, although it stresses that the transfer of sovereignty and government back to the Iraqi people will happen as soon as practicable.
The United Nations is promised a strengthened vital role in the political and economic reconstruction process, but only as circumstances, particularly security, permit.
Still missing is a clear timetable, with dates, for a transfer of power and anything like the more dominant role that the UN had sought, our correspondent says.
But the resolution asks Iraqi leaders to draw up a
plan for a new constitution and elections by 15 December.
The three dissenting countries had raised concerns about the role the United Nations would play in the political settlement in Iraq, as well as about the mandate of a future international peacekeeping force.