Non-EU-citizens who want to study longer than 3 months in Germany are required to get a residence permit for study purposes (in case they did not already get a visa that is valid for the whole time of their stay). This applies equally to non-EU-citizens who got an entry visa before coming to Germany (which expires after 3 months) and to those who need no visa to enter the country.

As a non-EU-citizen you must apply for the residence permit for study purposes within 3 months upon your arrival. You do this at the "Ausländerbehörde" (Immigration Office) directly. Should you have any questions, though, you can send an email to binstud@international.tu-berlin.de or visit my colleagues from the TU Berlin visa advising unit during their office hours in room H51.