At a polling station at Lillholms school in Skärholmen, southern Stockholm , 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 thousands travelling from Norway and Finland to different areas 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 causing problems.
Voting was held in 16 countries across the globe. In Iraq, election day saw the country hit by multiple attacks, with at least 35 people being killed.
Sweden sent six electoral observers to the country.