A surge in the number of people crossing into Turkey has increased the total by one million in just 10 months.
More than seven million others have been displaced inside Syria since the start of the uprising in March 2011.
The head of the UN’s refugee agency, Antonio Guterres, called it the “worst humanitarian crisis of our generation”.
The refugee crisis is the largest resulting from a single conflict in nearly a quarter of a century.
More than 230,000 people have also been killed in the past four years, activists say.
The UN High Commissioner for Refugees (UNHCR) said Turkey is home to the largest number of Syrians refugees – 1.8 million – and is reportedly preparing for a new influx as the conflict escalates near the border between the countries.