As a citizen of Greece, you benefit from the European Union's freedom of movement — one of the most significant rights in the EU legal order. You can live, work, study, or retire in Germany for any length of time without obtaining a visa, residence permit, or work permit. The only administrative step required is registering your address at the local Einwohnermeldeamt (Anmeldung) within two weeks of arrival, and enrolling in health insurance if you are employed.