Ghost has an advanced approach to migrating to Ghost from WordPress, and have written a plugin to make this happen smoothly. It still requires exporting data to a computer and re-uploading it, but Ghost's plugin helps access and format the data for a better transfer.
According to Ghost's guide, "Keep in mind that a migration from WordPress will not include custom fields, metadata, shortcodes, custom post types & taxonomies, or binary files. Just posts, pages, text, and images."
Also note that the user must fix URLs manually.
The source code (markdown) for this article can be found on GitHub.