They no longer put your address on your license. You have 30 days to update your address when you move. It will change from 'resident' to 'non-resident' after a period of time elapses once you become a resident of Tenn. Don't know what that time period is but you should be able to get that information from Tenn.
Once you are a resident of Tenn. your, then, non-resident Florida license will be treated as such. i.e. some states only recognize the licenses as valid if the individual is a resident of the issuing state.