Migration Minister Tobias Billström on Thursday announced that the government had submitted a proposed bill to the legal council, Lagrådet, which examines whether new laws are compatible with existing legislation. From there, the bill would be passed on to parliament for a vote.
If the legislation passes the Riksdag, a foreign PhD student who has spent four of the past seven years employed as a researcher will be able to apply for permanent residence.
"It has been a very important question for international PhD students and international students overall to get these dated, very antiquated rules changed," said Erik Pedersen, vice chairman of Sweden's Student Union Association.
Currently, PhD students have a slim window - ten days - in which to find work after completing their studies. The system has applied in the same way to them as it has to undergraduates or master's students, the student union noted. If the foreign researchers failed to find work after defending their thesis, their visa simply ran out.
"It's an odd starting point, as the PhD students work and contribute to the universities' research," Pedersen told The Local. "To consider what they do as not being equal to other employees means you value their work differently."
The head of the students union's PhD committee, Johan Svantesson Sjöberg, has been critical of the system for years.
"You've thrown people out for no reason," he told The Local. "It's bad for the individual, but also bad for Sweden."
There are roughly 5,000 foreign PhD students in Sweden, revealed a tally by Statistics Sweden in 2013.
Svantesson Sjöberg said that many of them took to the Facebook page Equality for foreign PhDs in Sweden to discuss the news on Thursday that the government has moved forward on visa reform.
"Until it is approved, there is no point to be satisfied..," one commenter wrote on the page.
The issue has been so contentious that several foreign PhD students took to the streets of Stockholm and Gothenburg to protest against the rules earlier this week.
"It is a pity that these highly-skilled scholars need to hit the streets to ask for their rights!" a page member wrote.
The migration minister told the Svenska Dagbladet newspaper that the reform would help make Swedish higher education more competitive globally. Last week, two of three Swedish universities on the Times Higher Education ranking fell off the list entirely.
"We have lost competence and knowledge with the rules that we had," said student union vice head Pedersen. "The rules weren't adapted to today's world where it's so easy to move between countries."