The resolution, submitted by the United Kingdom, was the subject of tough negotiations, and was amended several times before the vote on Friday.
The resolution also endorsed the results of UN-brokered peace talks in Sweden last week, when Yemen’s warring parties agreed to a ceasefire that took effect on Tuesday.
A withdrawal of fighters in Hodeidah, a key gateway for aid and food imports in the impoverished nation, was a part of the truce.
The ceasefire between Saudi-backed government forces and Houthi rebels is seen as the best chance yet of ending four years of Yemen’s devastating conflict.
The agreement also included a planned prisoner swap involving some 15,000 detainees.
After Friday’s meeting, Karen Pierce, Britain’s ambassador to the UN, said UN ceasefire monitors were needed in Hodeidah urgently and a core group of them would be dispatched to Yemen within days.
In a second phase, Guterres would have one month to determine the full size and scope of the mission and how it will ensure troops vacate the city and port, Pierce told Al Jazeera.
Guterres “is going to deploy an advance team first and that team will go in the next few days”, said Pierce. “He needs to get people there quickly and therefore the Security Council has been willing to authorise for 30 days an advance team.”
Later, the UN chief will “submit plans for a larger monitoring mission”, she added.
French ambassador Francois Delattre said the unanimous vote sent a “strong signal of the council’s unity and engagement” on Yemen, and that it had put its weight behind the UN-brokered talks.
Diplomats said the UN observer mission could consist of 30 to 40 people, tasked with ensuring the withdrawal of the warring parties from Hodeidah and the safe passage of humanitarian aid.
The observers will head up monitoring teams made up of government and rebel representatives, under the auspices of a Redeployment Coordination Committee headed by Cammaert.
Yemen, the Arab world’s poorest country, has been devastated by a multisided conflict involving local, regional and international actors.
The conflict began with the 2014 takeover of the capital, Sanaa, by the Houthis, who toppled President Abd-Rabbu Mansour Hadi’s government.
A Saudi-UAE-led coalition allied with Yemen’s internationally recognised government has been fighting the Houthis since 2015.
Since then, more than 60,000 people have been killed in the fighting, according to estimates by rights groups.
On December 8, the UN said that as many as 20 million people in Yemen were “food insecure”, calling the situation the “world’s worst humanitarian crisis”.
Louis Charbonneau, the UN director for Human Rights Watch, said the resolution “sends an important message to the suffering people of Yemen that they haven’t been forgotten”.
Additional reporting by James Reinl in New York City.