There’s a fairly functional piece of software that’ll get you pretty close to a complete migration (save for the images in your posts). The requirement (using this solution) is that the server hosting your WordPress must have access to the database of your old Joomla installation.
Have a look here: https://www.joho.se/index.php?/archives/338-Converting-from-Joomla-to-WordPress-up-to-2.7x.html
-joho
