France and Germany have said they will back the latest draft resolution on Iraq's future when the UN Security Council votes on it later in the day.
The issue of control of foreign troops was a key obstacle
Russia and China have also indicated they approve of it.
Correspondents say the draft removes one of the last obstacles to the deal, spelling out the relationship between Iraq's government and foreign forces.
It includes an undertaking that the US-led coalition will consult Iraqi leaders over major military actions.
That was a key demand for France which, like Russia and China, has a veto.
French Foreign Minister Michel Barnier said his country still had some reservations but these would not prevent it casting a vote in favour.
His German counterpart, Joschka Fischer, said he welcomed the imminent agreement and that Germany would vote for the resolution.
"I hope that now there will finally be a stabilisation of
the security situation in Iraq," he said.
Russian President Vladimir Putin said the resolution had changed for the better.
"It seems to me there is every reason to believe that this work could end with a positive result," he said during a visit to Mexico ahead of the G8 summit.
Chinese Foreign Minister Li Zhaoxing said positions on the draft were "coming close".
The US ambassador to the UN, John Negroponte, said earlier that Washington and London had made a major effort to take the views of various delegations into account during the closed-door consultations.
Provides for "full partnership between Iraqi forces and the multinational force"
Acknowledges need to confer on "sensitive offensive
Firmly places Iraqi security forces under Iraqi control
"We are putting it to a vote on Tuesday afternoon," Mr Negroponte told reporters during a pause in the discussions.
Addressing the Security Council before it began discussing the draft, UN Iraq envoy Lakhdar Brahimi said it would take eight months from the time of forming an interim government before credible elections could take place.
"The solution to Iraq's current challenges will take years, not months to overcome," he said in a report on his fact-finding mission to Iraq in April.
The US rejected a proposal by France that would have given Iraq a virtual veto over operations by coalition forces in Iraq after the 30 June handover.
But later, the text was amended to cover "the full range of fundamental security and policy issues, including policy on sensitive offensive operations".
Iraqi Foreign Minister Hoshyar Zebari has told the BBC that the new resolution will allow for closer co-operation on key security issues.
"What we are talking about here is really major offensive military operations that would have serious political consequences like Falluja," he told Radio Four's Today programme.
"We believe that we as Iraqis understand the situation better on the ground."
The newly appointed Iraqi Prime Minister, Iyad Allawi, and US Secretary of State Colin Powell had already promised in letters to the Security Council to reach agreement on policy for dealing with sensitive offensive military operations.
But they did not spell out whether the Iraqis would have to give their consent to each operation, or what would happen if they did not agree.
In his letter, Mr Allawi repeats his request that foreign troops stay "until we are able to provide security for ourselves".
The letter says a ministerial body will be established to "co-ordinate [with the multinational force] on all security policy and operations issues".
In his letter, Mr Powell pledges to co-operate with Iraqis "on the full range of fundamental security and policy issues, including sensitive offensive operations".
The fourth draft of the resolution states that the mandate of the multinational force will expire after elections are held in Iraq, no later than 31 January 2005.