Create an API User in your Magento store admin that has read access to your catalog. (Instructions included)
Then install this search plugin in your Joomla.
Add the username and password of the API user to your search plugin.
When people search for keywords that are in your products, your Magento products will be supplied within your Joomla search results.
Click here for video demos of this product. This is a downloadable product so you can download it after paying with a credit card.
Product Tags
Add Your Tags:
Use spaces to separate tags. Use single quotes (') for phrases.