According to Article 21(1) of the Treaty on the Functioning of the European Union, every EU citizen, like you, has the right to move and reside freely within the territory of the EU, subject to the limitations and conditions laid down in the Treaties and by the measures adopted to give them effect. EU citizens are entitled to reside in Greece for 3 months; the only condition is that they must be in possession of a valid ID card or passport. EU citizens may remain for longer than 3 months if they are employed or self-employed in Greece; they are students or are in vocational training or are unemployed, provided they have sufficient funds and health insurance; they are family members, regardless of nationality. Furthermore, third-country nationals who are family members of an EU citizen must submit an application for a residence document within 3 months of arrival. So you apply as an EU citizen for the respective residence permit and your wife afterwards as your family member.
