Working remotely from Europe for a US company

Hi,

 

I am an Alaskan resident and I have dual citizenship (US & Cyprus which is part of the European Union). I am currently working remotely from Alaska for a company based in California. 

 

I have recently decided to move to Cyprus and my employer would like to keep me employed as a full time employee, and let me continue working remotely from Cyprus instead of Alaska.

 

Will my employer be able to have me working as a full time employee, with the same employment terms and can I continue paying taxes as if as I am living in Alaska, since that is the state that I have been paying taxes in the last 7 years? 

 

I do understand that a US citizen can work remotely from Europe for up to 3 months, since that is the period that a US citizen is granted a tourist visa to stay in Europe, but since I am a European Union citizen I don't have any visa restrictions.

 

Thank you!

 

Sergios