Syrians desperate to leave their war-engulfed homeland are forced to pay hefty bribes at armed checkpoints proliferating along Syria's borders, or to smugglers, the UN refugee agency said.
The record figure is one million refugees more than a year ago, while a further 6.5 million are displaced within Syria, meaning that "almost half of all Syrians have now been forced to abandon their homes and flee for their lives," it said.
"The Syrian crisis has become the biggest humanitarian emergency of our era, yet the world is failing to meet the needs of refugees and the countries hosting them," said Antonio Guterres, UN High Commissioner for Refugees.
Hollywood actress Angelina Jolie, who serves as UNHCR special envoy, said in a separate statement: "Three million refugees is not just another statistic. It is a searing indictment of our collective failure to end the war in Syria."
The vast majority of Syrian refugees remain in neighbouring countries, with the highest concentrations in Lebanon (1.17 million), Turkey (830,000) and Jordan (613,000), the UNHCR said.
Some 215,000 refugees are in Iraq, with the rest in Egypt and other countries. Syrians have also been among migrants who have drowned in the Mediterranean while trying to reach Europe, Ms Jolie said.
The host governments estimate that hundreds of thousands more Syrians have sought sanctuary in their countries without formally registering, the agency said.
But there are worrying signs that the journey out of Syria is becoming tougher for desperate families, it added. Some areas of Syria are emptying out as the front lines in the conflict shift.
"Recent arrivals to Jordan, for example, are running from attacks in the areas of al Raqqa and Aleppo," the UNHCR said.