In short, yes. If you have a residence permit as a student you can bring your family to Iceland with you. There, however, some rules which you can find below.
Obtaining a student visa yourself
People who are not from the European Economic Area (EEA) or EFTA (Iceland, Switzerland, Liechtenstein and Norway) and want to study in Iceland for more than three months are obliged to file for a student residence permit. Usually, the student residence permit is valid depending on their enrolment and ability to financially support themselves. So if you can prove higher means of financial support, your permit will also be issued for longer.
To be eligible for a student permit, you must be 18 years and older (exchange students may be younger), and be admitted into studies that are recognised by the Directorate of Immigration. Those can be full-time studies at an Icelandic university, postgraduate studies at a university outside of Iceland that collaborates with an Icelandic university, exchange programmes, internships where working in Iceland is part of your studies, and technical studies at higher education institutions.
You should apply for a residence permit for your studies before June 1 for the autumn semester and before November 1 for the spring semester each year. That way there is enough time for the permit to be processed before the semester commences. The application form can be accessed via Island.is and needs to be submitted in paper form to the Directorate of Immigration. Before handing in the application, you also need to pay a processing fee of ISK 16,000 for your application to go through.
In your application for a student residence permit, you need to show that you have enough financial resources for your entire stay. So if you stay for one year, you also need to prove that you can support yourself for that time. In your application, you need to attach a transcript from your bank account with the specific amount. The Directorate of Immigration has specific requirements for how much money is needed for an individual to live in Iceland. For an individual, the minimum amount required is ISK 217,799 per month [EUR 1,441 / USD 1,604].
Bringing the whole family to Iceland
According to the Directorate of Immigration, you have the right to bring your marital spouse or your cohabiting spouse (defined as a cohabiting partner of at least one year). If you have children under 18 and have custody of them, you are also allowed to bring them to Iceland. Likewise, if your parents are over the age of 67, you also have the right to family reunification with them.
In order to have all the paperwork sorted, your family members need to apply for a residence permit to the Directorate of Immigration. This can only be done in paper form to the address of the Immigration office. Additionally, they also need to pay a processing fee of ISK 16,000. To bring your entire family to Iceland, you need to prove that you can financially support them for their entire stay.
For a couple, this means a minimum monthly amount of ISK 348,476 [EUR 2,306 / USD 2,566] and another ISK 108,898 [EUR 720 / USD 802] for every additional family member above the age of 18. For children under 18, there are no requirements for providing independent financial support. It is important to note that payments in the form of social assistance, alimony payments, support by a third party, assets other than bank account balances (e.g. real estate) and cash are not considered secure means of support.
What costs can you expect?
Minimum yearly budget for a couple $30,792 / €27,672
Minimum monthly budget: USD 2,566 / EUR 2,306
Minimum yearly budget for kids under 18 $0 / €0
No requirement to showcase independent financial support
Minimum yearly budget extra adult $9,624 / €8,640
Minimum monthly budget for family member above 18: USD 802 / EUR 720
Total minimum for a year $40,416 / €36,312
Total minimum costs for bringing yourself, a spouse and an adult family member
So if you’re thinking of bringing your spouse, your parent and your two kids to Iceland with you while you’re studying you should expect to be able to prove a minimum monthly budget of ISK 457,374 [EUR 3,027 / USD 3,368]. if you intend to stay for one year and also receive a student permit for that timeframe, you need to multiply that amount by twelve. So in total, you need to be able to showcase a whopping 5,5 Mio. ISK [EUR 36,312 / USD 40,416] on your bank account.
Please keep in mind that this is merely the minimum amount required by the Directorate of Immigration for your application to be processed. Housing and living in Iceland are rather expensive. So don’t expect too comfortable of a lifestyle with those funds! You better start saving early.