Hi Derek,
Are we talking about WHM/cPanel or what?
WHM/cPanel backups will copy to a remote FTP. I've never actually used it but it does have the functionality. You would want to watch your disk space though as I don't think it deletes the backups after copying them to the FTP site.
If not WHM/cPanel I'm sure you could find scripts online to do it, maybe even write one yourself.