There are polling stations in Stockholm, Södertälje, Malmö and Gothenburg. Sweden has 31,045 expatriates registered to vote.
At a polling station at Lillholms school in Skärholmen, southern Stockholm on Saturday, people waited in line to vote before lunch.
Samir Al-Karavi told Swedish public service radio news Ekot why the election day is important.
"It means a lot. I am very happy. I want to live like we live here in Sweden. We want to build a country so that all Swedes knows that our country is a good country."
Some Iraqi nationals had to travel great distances to have their say with the polling booths in Stockholm the nearest for those living in Norway, Finland and the north of Sweden.
Haidar Al-Tamimi travelled with his friends from Helsinki and told Ekot that they had problems getting there on the ferry with the heavy ice sheets in the Baltic sea.
Voting is being held in 16 countries across the globe. The United Nations refugee agency estimates that around two million Iraqis are living abroad, with an estimated 80,000 + living in Sweden.
Meanwhile Sweden has sent six electoral observers to Iraq.