The council is expected to vote on the measure next week, diplomats aid.
The mission would provide for the deployment of up to 75 monitors in the rebel-held city of Hodeida and its port along with the ports of Saleef and Ras Issa for an initial period of six months, according to the draft obtained by AFP.
Talks between the Saudi-backed government and Huthi rebels last month in Sweden on ending the devastating war led to an agreement on the observer force.
A first group of about 20 monitors has been authorized by the council to begin work in Yemen, but their mandate was only for a month.
The UN says a ceasefire that went into force on December 18 in Hodeida has been generally holding, but there have been hurdles in the way of redeploying rebel and government forces from the city.
The draft calls on UN Secretary-General Antonio Guterres to "expeditiously" deploy the full mission, led by retired Dutch General Patrick Cammaert.
UN envoy Martin Griffiths told the council on Wednesday that "substantial progress" was needed to shore up the ceasefire before a second round of talks could be held.
Under the Stockholm deal, the sides were to meet again later this month, but that has now been pushed back to February, diplomats said.
The new United Nations Mission to support the Hodeida Agreement (UNMHA) will be tasked with supporting the Stockholm agreement by overseeing the truce, forces pullback and ensure the security of the city and ports.
The port of Hodeida is the entry point for more than 70 percent of Yemen's supplies of imported goods and humanitarian aid.
The war has unleashed the world's worst humanitarian crisis, according to the UN, which says 80 percent of the population -- 24 million people -- are in need of aid.
Nearly 10 million people are just one step away from famine, according to UN aid officials.
The conflict between the Huthis and troops loyal to the government escalated in March 2015, when President Abedrabbo Mansour Hadi fled to Saudi Arabia and the Riyadh-led coalition intervened.