Under the new law, it will be harder for those who applied for asylum after 24 November last year to receive a permanent residence permit.
Instead, those granted asylum will be given three-year residence permits that have the potential to be extended if they are deemed to still be in danger if they return to their homeland. If they have shown that they can support themselves they could be granted permanent residency.
The rules on family reunification have also been tightened.
The law, which will be in effect for three years, means Sweden will observe the EU’s minimum level of rights for asylum seekers.
"It's an extremely radical shift," said Anders Hellström, an associate professor in political science at Malmö University, who's affiliated to the university’s institute of migration. "In the beginning it (Sweden) was really generous, but now it's really restrictive."
There has been strong criticism of the law from human rights groups and there were protests outside of parliament on the day the law was passed.
Last year, Sweden received a record 163,000 asylum applications, before sharply reversing its border policy as it struggled to cope with the influx.
There has been a significant drop off in the amount of asylum applications received in 2016. So far this year, there have been 16,800 applications, which is less than half the amount at the same time last year.
Hellström speculated that may be because Sweden's reputation has changed among those planning to seek asylum.
"Maybe you heard before that Sweden was an exception, but now Sweden is no longer an exception," he said.