In order to qualify, applicants would have to be in full-time education. Alternatively, they must have previously been studying, and now have the intention to take up their studies again. Both academic and vocational studies would be acceptable.
They would also have be present in Sweden and able to demonstrate a clean criminal record.
Successful applicants would be granted temporary residence permits enabling them to complete their studies. They would then be given the chance to convert these into permanent permits, upon finding a job.
Those over the age of 18 would also be eligible to apply, as long as they were under 18 before 24 November 2015.
The proposal was announced by Deputy Prime Minister Isabella Lövin, Labour Market Minister Ylva Johansson, Education Minister Gustav Fridolin and Minister for Migration Heléne Fritzon in Stockholm on Monday afternoon.
The Greens had long been campaigning to lift restrictions on unaccompanied minors, but until now had been unable to reach an agreement with their Social Democratic governing partners.
Minister for Migration Heléne Fritzon confirmed that those who arrived after 24 November 2015 would not be affected, and ruled out a general cancellation of deportations.
The proposal can only enter into force with the support of other parliamentary parties.