You can force an HTTPS connection on your Joomla! website by adding the following lines in the .htaccess file of your application.
++++++
RewriteEngine on
RewriteCond %{SERVER_PORT} !^443$
RewriteRule .* https://%{HTTP_HOST}%{REQUEST_URI} [QSA,R=301,L]
<IfModule !mod_ssl.c>
Redirect permanent / https://www.yourdomainname.com
</IfModule>
+++++++
Make sure that you replace www.yourdomainname.com with your actual domain name.