Margaret Beckett, the British foreign minister, said on Friday that there was "an agreed text" and the full UN Security Council would receive the draft later in hopes of a vote later in the day.
US State Department spokesman Sean McCormack said Condoleezza Rice, the secretary of state, welcomed the agreement.
"That is a positive step forward but it is only one step in this process. We want a vote on this resolution that will lead to a lasting resolution," McCormack said.
Israel and Lebanon have received copies of the draft resolution.
Ehud Olmert, the Israeli prime minister, will ask his cabinet to approve the UN proposal on Sunday.
The Lebanese government will examine the resolution on Saturday but a source denied that it had already given the green light to the text.
In principle, the resolution meets the essential demands of the government in Beirut.
The agreement calls for an immediate "cessation of hostilities" followed by a phased withdrawal of Israeli units as the Lebanese army and an expanded UN peacekeeping force move into the south.
A deal on a resolution had been delayed over the timing of an Israeli withdrawal from south Lebanon.
Beirut wanted a quick Israeli pullout, but Tel Aviv had said a strong multinational force must be deployed first.
The latest compromise calls for a phased Israeli withdrawal as the Lebanese army moves into the south. At the same time, the UN Interim Force in Lebanon would be reinforced by up to 15,000 French and other troops.
As part of the deal, Hezbollah would pull out from south of the Litani River, 20km from the Israeli border.
More than 1,000 Lebanese and 121 Israelis have been killed in the five-week war that began on July 12.
At the insistence of Lebanon, the United States and Britain agreed to drop a reference to Chapter 7 of the UN Charter, which permits a robust UN peacekeeping operation.
But Emyr Jones Parry, Britain's ambassador to the UN, said the text would carry strong rules of engagement for the expanded force that France is expected to lead.
Beckett cautioned that the resolution, expected to take a week to implement, was a short-term one. "We're not here trying to solve all the problems of the Middle East overnight."
A second resolution on a permanent ceasefire is to follow within a month, tackling a range of outstanding issues.