I still have a PA driver's license, but have been living mostly in FL for 4 years. If I become a Florida resident now, can I file my 2018 taxes as a Florida resident?

Florida does not have a personal income tax so there is not a Florida state income tax return to file.

Your state residency isn't determined by your driver's license.  It's determined by the location of your main or primary home, which is known as your domicile in tax terminology.  If your main home has been in Florida for 4 years, you've been a Florida resident for 4 years.

BTW, Florida law is that you must obtain a Florida drivers license within 30 days of establishing residency in Florida.