Greece is a member of the Hague Adoption Convention since 2010. If you are a U.S. citizen and want to adopt a Greek kid you should follow the procedure laid down in the Convention.

Not many kids from Greece have been adopted through intercountry adoption. In Greece there are no private adoption agencies. The procedure of adopting requires a gynecologist who will act as a facilitator and a lawyer. Kids can be adopted from government or privately-run institutions and orphanages. You must be found eligible to adopt by the Department of Homeland Security, U.S. Citizenship and Immigration Services (USCIS). In addition, you must be a resident of Greece, between the ages of 30 and 60 (at least one of the adoptive parents must be at least 18 years older but not more than 50 years older than the adopted child) and you must provide information about your financial status. There is no requirement about marriage of the adoptive parents. There are no post-adoption reporting requirements. The adopted kid must have legitimate U.S. passport to enter or leave the United States.

Some airflight companies offer various adoption airfare discounts to help the adoptive parents who are trying to work out the high expenditures of the intercountry adoption. The adoption fares are also more flexible, with no fees or penalties on itinerary change, changes in the date or time of travel etc. When booking a flight, ask for such adoption airfare programs and its conditions.