I am moving to Virginia from where I am fortunate enough to be able to work remotely for a company in Florida. Florida has no state income tax. Do I have to pay Virginia state income tax?
Yes, as a Virginia resident you must pay income tax on income earned outside Virginia. If you pay income tax in another state, you can claim a credit in Virginia. However, because Florida has no state income tax you will not have to file in Florida and you will not claim the credit in Virginia. From the VA form 760 instructions:
As a Virginia resident, all of your income is subject to the Virginia Individual Income Tax, regardless of where it was earned or its source. However, if you received income from another state and are required to file a nonresident return in that state and pay income taxes, you may be eligible to receive a credit for the taxes paid to the other state.
Keep in mind that if you move to VA this year you will file a form 760PY, partial-year resident return. Virginia will only tax you for the income you earned while you lived in VA, not for the whole year. VA has special agreements with certain other states, such as California, but Florida is not one of them. I'm a VA resident and I had income in California last year, and I ended up hiring an accountant to prepare my taxes to make sure I got it right.