I keep all my genealogy related files in Dropbox so I can work on it anytime, anywhere, any of my computers. I have FTM installed on all of them. Since the working FTM files are in dropbox, and most importantly locally on each computer, every change I make from any computer gets synchronized with all computers.
This way there is a current copy always on each computer and one on line so that also gives me redundant backups.
So you could move your files into a dropbox folder and then use it to get your files to the new computer. And leave them on the old one, too, if you are still using it.