The country now plans to welcome 2,000 Syrians this year, that is 500 more than previously planned, followed by 3,000 each year in 2016 and 2017.
The new figures aim to meet a quota set by the UN refugee agency UNHCR.
A compromise came after long discussions between the right-wing minority government, which had opposed allowing in any more refugees, and centre and left-wing parties, which wanted to accept 10,000 people in two years.
Under the agreement, financial aid will be distributed to the country's regions to encourage them to give shelter to those fleeing Syria's four-year war.
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Another 5,000 refugees who have already been granted residence permits in Norway are still living in community shelters, and need to be given homes.
"This is an important step in the right direction," the Norwegian Refugee Council aid agency said in response to the announcement.
"NRC now urges other European countries to follow. With some exceptions, like Germany, the European countries have done far too little in response to the largest humanitarian crisis in our generation," it added.
The UNHCR has called on the international community to resettle more people fleeing Syria's civil war, which it says has triggered the largest humanitarian crisis since World War II.
Nearly four million Syrians are registered with the UN as having fled into neighbouring countries since the conflict broke out in 2011.