if you work and live in GA, you would only pay taxes to GA.  

in the year you move, there would be tax returns required for both NY and GA, but that is nothing out of the norm for people that move between states.

or, are you saying you are going to remain in NY to both work and live.  In that case, you'd pay taxes to NY only.  

I will continue living in NY and working remotely from NY, but the company I will be an employee of is located in GA.  So as long as I am physically working from NY, I only have to pay NY state taxes, correct?

@netbeans - I guess that 'working remotely from NY' throws me 

simply, if you work and live in NY - regardless of where the Company's HQ or regional office is, you will pay NY income tax and not GA. 

You are not stepping foot in GA , so no tax to be paid there.  

I agree with NCperson, you only pay tax, on that income, to NY.  You do not file a GA return, unless your employer mistakenly withholds GA tax.  Then, you would only file a GA return to get a refund. Try to address the state withholding with your employer up front.

A handful of states (New York, Pennsylvania, Nebraska, Delaware and Arkansas) tax telecommuters. GA is not one of them. 

To add to @Hal_Al's answer, if your employer cannot or does not withhold NY taxes from your pay, you'll have to pay quarterly estimated taxes to NY.

https://www.tax.ny.gov/pit/estimated_tax/who_must_make.htm