"It's going to make a big difference. We are now using just one crossing," a spokesman for UN Secretary General António Guterres told the BBC.
The quake in neighbouring Turkey is known to have killed almost 40,000 people in the two countries.
Many Syrians have been angry over the lack of aid to their war-torn nation.
The government of President Bashar al-Assad has blamed difficulties in rescue efforts on the impact of Western sanctions imposed on the country.
But international aid groups say the key impediments are the Assad government's mismanagement and refusal to engage with all areas of the country.
More than 5,700 people are now known to have been killed in Syria by the 6 February earthquake.
In Turkey, the death toll has already exceeded 31,000.
More than one million people have been left homeless in Turkey, and in Syria this number could be much higher, aid organisations warn.
Rescue teams in both countries are now winding down rescue operations in the vast area, as chances of finding any more survivors are fading.
Crisis upon crisis: Why it's hard to get help to Syria
The UN made an announcement about the two new border crossings - in Bab al-Salam and Al Ra'ee on the border with Turkey - after high-level talks with President Assad in Damascus on Monday.
It said the crossings into rebel-held north-western Syria would initially be open for three months.
"Very shortly we will use the other two crossings," Mr Guterres' spokesman Stéphane Dujarric told BBC Radio 4's World Tonight programme.
"We hope that the agreement will last as long as we need to use it. We will start using it as quickly as possible and I don't want to make any assumptions, the only thing I want to assume is that people will put politics aside wherever they stand in this conflict."
He did not give any further details on when the two crossings would open.
And Mr Dujarric defended the delay in waiting for Syria's permission to open the crossings.
"It is our understanding that other aid organisations not affiliated with the UN have been using these border crossings. We have to operate within certain perimeters, that's the nature of the United Nations.
President Assad has made no public comments on the issue.
In the first few days after the quake, some supplies reached the government-controlled areas of Syria, primarily from friendly countries like Russia, Iran and the United Arab Emirates.
But the devastated north-western rebel-controlled areas of Syria remain virtually cut off.
This is because international humanitarian aid to these parts can only arrive through a single crossing from Turkey or through the government-controlled areas of Syria.