The UN Security Council has agreed to deploy a team to the Yemeni port of Hudaydah to oversee a ceasefire there.
The truce began on Tuesday after being agreed at UN-sponsored talks last week between delegations from the Yemeni government and Houthi rebels.
Britain drafted the UN resolution, the first on Yemen for three years.
It was approved after negotiations during which the US pushed for the resolution to be stripped of language calling for war crimes accountability.
The UN team will be deployed for an initial 30 days to monitor and help implement the ceasefire deal.
What is happening in Hudaydah?
Hudaydah, 140km (90 miles) west of the capital Sanaa, was Yemen's fourth-largest city and a major economic hub before rebels took control of it in late 2014.
As a port, it is also a lifeline for just under two-thirds of Yemen's population, who rely almost entirely on imports for food, fuel and medicine.
It is one of the areas controlled by the rebels, but since June has been under assault by a Saudi-led coalition backing the pro-government troops.
More than 22 million Yemenis need some form of aid, and eight million do not know how they will obtain their next meal.
What does the resolution say?
The final resolution "calls on the government of Yemen and the Houthis to remove bureaucratic impediments to flows of commercial and humanitarian supplies, including fuel, and on the parties to ensure effective and sustained functioning of all of Yemen's ports".
It also asks UN Secretary General Antonio Guterres to submit proposals by the end of the month for a substantive operation to monitor the ceasefire and the redeployment of fighters from Hudaydah, and also play a leading role in the management and inspections of three of the city's ports.
The BBC's UN correspondent Nada Tawfik says the UN believes peace in the Red Sea port could help relieve the suffering of millions facing starvation, and ultimately help bring the civil war to an end.
What were the US-UK disagreements?
The US had been unhappy with the UK-drafted resolution and came up with its own draft version on Thursday, which removed references to the humanitarian crisis in the country.
The US also wanted to condemn Iran for breaking an arms embargo on Yemen but Russia objected, Reuters quoted diplomats as saying. Iran denies sending weapons to the Houthis.
To reach a final agreement, the UK had to remove reference to the "need for transparent, credible and timely investigations into alleged violations of international humanitarian law" and for those responsible to be held accountable, Reuters said.
The Saudi-led coalition backing the government of Abdrabbuh Mansour Hadi has been carrying out air strikes - backed by Western nations including the US, UK and France, which have provided logistical and intelligence support.