The UN High Commissioner for Refugees said the number of people seeking haven in neighboring countries had jumped since the beginning of the year.
Half of the refugees were children, the UN said, most of them under 11 and often traumatized by their experiences.
The largest numbers of refugees were seeking shelter in Jordan, Lebanon, Turkey, Iraq and Egypt.
The figure includes registered refugees and newer arrivals awaiting registration.
“Syria is spiraling towards full-scale disaster,” the UN High Commissioner for Refugees Antonio Guterres said in a statement, warning that the international humanitarian response capacity was “dangerously stretched”.
“This tragedy has to be stopped,” he added, warning that the influx of people had also stretched the resources of Syria’s neighbors.
The millionth refugee recorded by UNHCR was a 19-year-old mother of two called Bushra.
“Our situation is so bad, everything is so expensive, we can’t find any work… The situation is so bad, I live with 20 other people in one room,” Bushra told reporters in the Lebanese city of Tripoli.
Many of those who have fled conflict now live in difficult conditions, with poor sanitation and insufficient resources to cope with the harsh winters.
In Lebanon, for example, the influx of almost a third of a million refugees since last February has swollen the country’s population by 10%.
Turkey, providing a temporary home for some 184,000 refugees, has spent more than $600 million setting up 17 refugee camps, and was building new ones to meet the increasing need, the UN said.
“These countries should not only be recognized for their unstinting commitment to keeping their borders open for Syrian refugees, they should be massively supported as well,” Antonio Guterres said.
On Tuesday, King Abdullah of Jordan called on world nations to help his country, Turkey and Lebanon to shoulder “the tremendous burden” of caring for the huge influx of people.
UK charity Oxfam says that only 20% of $1.5 billion promised by international donors in January has arrived, “leaving agencies struggling to respond to the urgent needs of refugees”.
The rush of refugees has surprised even UN experts, who had originally estimated that the one million figure would not be reached until the end of June 2013.
In effect, more than 400,000 have became refugees since 1 January 2013.
The UN’s emergency response plan for Syrian refugees, it said, currently lacked 75% of the funding required.
Jordan’s Petra news agency said that a total of 2,257 Syrian refugees had crossed into the country on Tuesday alone.
Some 110,000 of those who have sought shelter in Jordan are living in the desert camp of Zaatari, near its northern border with Syria.
The conflict in Syria began almost two years ago with demonstrations against the government of President Bashar al-Assad.
The protests quickly turned violent as opponents of Bashar al-Assad took up arms to try to resist a brutal crackdown by the authorities.
The conflict has left more than 70,000 people dead and two million internally displaced.
Also on Wednesday, the Commander of the rebel Free Syrian Army, General Selim Idriss, has called for the lifting of the EU arms embargo against Syria, saying it is having a much more negative effect on the opposition than on the Assad regime.
Gen. Selim Idriss said opposition forces desperately needed weapons and ammunition, and that the war would be longer and bloodier if the embargo remained in place.
Please consider making a donation to help the refugees: Syria crisis appeal on Oxfam’s page for Syria.
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