After moving your Joomla site to Wordpress platform, you need to edit your posts making them pretty, adding SEO meta tags, aligning pictures etc.
But the biggest concern is your URL structure. Search engines, including Google, do remember your old URLs, have them cached and hardly will index the same content under different URLs or give them significantly less value compared to the original URLs.
Let’s say you had on Joomla www.site.com/content/view/23/45
after moving to Wordpress you have something like www.site.com/contentview2345.
That’s the BIG issue
The solution might be as following:
1. Create HTML site-map of your desired (old Joomla) URLs, put it into footer of WP. Here is a useful plugin for generating HTML sitemaps in Wordpress.
2. Create XML sitemap with old Joomla URLs, here is useful plugin, and submit it via Google Webmaster.
3. Finally do the main thing: download and install Redirection plugin. Then manually, yes manually (are you scared of this word?:) make 301 permanent redirect of each WP URL to the desired (your old Joomla) URL.
Hope it helps.