Foreign motorists from any of the countries who are party to the United Nations Convention on Road Traffic (Geneva, 1949) and the Convention on the Regulation of Inter-American Motor Vehicle Traffic (Washington, D.C., 1943) who visit the United States as tourists can drive legally using their valid domestic driver's license for a period not to exceed one year from the date of arrival. They may drive either a personal or rental car.
Tourists from countries who are party to the Geneva Convention and the Regulation of Inter-American Motor Vehicle Traffic can also legally drive their own private cars bearing valid license plates/registration tags issued in their native country for a period not to exceed one year from their date of arrival.
Foreign tourists whose country is not among those that are party to the terms of either convention may be required to obtain a driver's license and secure license plates/registration tags upon arrival in the United States (U.S.).
Greece is a member of the Convention on Road Traffic so normally you should be able to use your valid driver's license from Greece for 1 year. The thing that might change the length of time you can use this international license is the fact that you are now a permanent resident of the US and not a tourist with a visitor status. Due to this you will need to contact the New Jersey Motor Vehicle Commission to find out for certain how long your international license that was issued by Greece is valid to drive on in NJ.
According to the New Jersey MVC you may use your country's driver license as proof of driving experience if you have an International Driver License issued by your country or if your country is a member of the United Nations Convention on Road Traffic and your license is translated into English by a consulate or an MVC approved translator.
You must also provide proof by the U.S. Immigration and Naturalization Service, authorizing your presence in the country and confirming validity of your foreign license. If you cannot show proof of driving experience you will be subject to NJ graduated driver's license (GDL) program requirements.
To find out more information on how long you can drive on your current foreign license and what you will need to do in order to obtain a NJ license contact the New Jersey Motor Vehicle Commission.
Once you receive your New Jersey license you can come here for a car insurance quote.