After weeks of negotiations, Australia, Jordan and Luxembourg drafted the text for a vote. Damascus's ally Russia, which has already used its veto on four Syria-related resolutions since the conflict began in March 2011, has no plans to do so this time.
"We are close to a very good agreement," said Rwandan envoy Eugene-Richard Gasana, who holds the council's rotating presidency.
Ahead of final negotiations, Russian ambassador Vitaly Churkin had also expressed optimism, saying there were only two items that were still "unacceptable" for Russia.
The shipments will travel through four different border crossings -- two in Turkey (Bab a-Salam and Bab al-Hawa), one in Iraq (Al-Yarubiyah) and another in Jordan (Al-Ramtha).
The United Nations accuses the Syrian regime of imposing bureaucratic and arbitrary obstacles to the delivery of humanitarian aid.
Because of the restrictions and ongoing insecurity, 10.8 million Syrians need help, of which 4.7 million live in hard-to-reach areas trapped by the fighting or under siege by government troops or rebels.
The proposed resolution sets a "monitoring mechanism" under UN chief Ban Ki-moon's authority to ensure that the "humanitarian nature of these relief consignments."
The UN estimates that the system would help provide food and medicine to between 1.3 and 1.9 million more civilians, most in zones held by armed rebel groups.
"The United Nations humanitarian agencies and their implementing partners are authorized to use routes across conflict lines and the border crossings... in order to ensure that humanitarian assistance, including medical and surgical supplies, reaches people in need throughout Syria through the most direct routes," the draft resolution said.
The authorization is valid for 180 days and must be renewed by the council.
Protracted negotiations over the text faced many hiccups, with Russia insisting that its Syrian ally be allowed to examine the operations, while Western countries pressed for the aid operations to be as fluid as possible.
And Damascus also faced a threat of further sanctions if it did not comply.
The text namely "affirms that (the council) will take further measures in the event of non-compliance with this resolution (or its predecessor)... by any Syrian party."