After you successfully pass the entrance exam, you receive an official notification from ELTE that you are admitted to the study program (a Letter of Acceptance document is issued and sent to you). Before you start your studies at ELTE, you need to ensure your legal status in Hungary. Depending on which part of the world you are coming from to Hungary, choose the appropriate way to make your stay legal.
If you are a citizen of an EU/EEA member state (EEA = EU member states and Norway, Switzerland, Iceland, and Lichtenstein), you may travel to Hungary without a long-term study visa, but you need to obtain a registration card for the duration of your studies in Hungary. For more information, visit: EEA students - Registration certificate
If you are a citizen of a country that is not part of the European Economic Area (EEA), you are required to obtain a residence permit, and you need to register your accommodation after your arrival in Hungary. For more information, visit: Non-EEA students - Visa/Residence Permit
After you arrive in Budapest, you can arrange your registration card (EEA) or residence permit (non-EEA) at the National Directorate-General for Aliens Policing (in Hungarian: Országos Idegenrendészeti Főigazgatóság), formerly known as Immigration and Asylum Office (in Hungarian: Bevándorlási és Menekültügyi Hivatal, abbreviated as BMH). In the office you can arrange registration card, prolongation of national permit, authority’s approval of invitation letter, report of accomodation.
Visiting address to National Directorate-General for Aliens Policing for students in higher education:
Branch Office III (Budapest)
Branch Office V (Budapest)
A short guide on how to book an appointment at the National Directorate-General for Aliens Policing is available here.