I think that you could use Box for this pretty effectively. With their $15/month business plan, you get 1TB of storage and can apparently set any directory as a "workspace", which presumably includes the home directory. For most users, that would be more sufficient to keep everything backed up and the syncing process is supposed to be the same kind of transparent deal as Dropbox (which would also be a good solution, except that you can't set an arbitrary directory as your Dropbox folder).
until it encrypts the workspace and that gets synced. Although, I suppose you might have a previous revision as I know dropbox supports versioning for some (all?) kinds of files.