"We have gotten all of the approval letters, we are ready to deliver," the UN agency's Syria representative Elizabeth Hoff told AFP.
While stressing the deliveries would still depend on the security situation, she described the approvals as "a big step forward."
The Syrian government and other parties to the conflict had agreed to allow and facilitate deliveries of medicine for chronic diseases, vaccines, intravenous fluids and surgical supplies to opposition-controlled areas in Aleppo governorate, the besieged Damascus district of Muadamiya, and the flashpoint Eastern Ghouta region near the capital.
Deliveries would likely first be made to opposition-controlled areas in Aleppo governorate, Hoff said.
She said she was "very optimistic" that a convoy of several trucks would bring the goods into Aleppo by next week, and that deliveries to the two other areas could happen within a couple of weeks.
The plan is to deliver around 28 metric tonnes of medical supplies to seven opposition-controlled towns in rural Aleppo and around 102 metric tonnes to Muadamiya and Eastern Ghouta, her office said.
Deliveries had picked up to Aleppo after the UN Security Council in July adopted a resolution allowing UN convoys to cross Syrian borders to deliver desperately-needed aid, but since September only a few small shipments had gotten through, Hoff said.
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Muadamiya has received just one delivery of medical supplies in the past two years, she said.
The health situation across war-ravaged Syria is critical and deteriorating and is particularly dire in areas largely isolated from aid, Hoff said.
An estimated 4.7 million Syrians are living in hard-to-reach areas, including 241,000 in places besieged by the government or opposition groups, according to UN estimates.
Hoff pointed to rising numbers of measles cases as vaccination coverage across the country has slumped from 90 percent before the conflict began in March 2011 to 52 percent.
And she said waterborne diseases were continuing to spread even in winter, serving as testimony of horrendous sanitation and hygiene situations.
"In some shelters for displaced people, 50 to 70 people share a single toilet," she said.
More than 200,000 people have been killed in Syria since the civil war began, and around half the population has been forced to flee.