To redirect all traffic that goes to a http site to your https site, you have to work with redirect.
If you are using Apache as your webserver, just edit the .htaccess file in your document root.
Be sure mod_rewrite is enabled in your setup.
Then, just simply add the following lines
RewriteCond %{HTTP_HOST} !^www\.YOURWEBSITE\.com$ [NC]
RewriteRule ^(.*)$ https://www.YOURWEBSITE.com/$1 [R=301,L]
For Nginx this needs a little bit more of effort.
Add the following lines into the the server {} configuration for your port 80 webserver within the virtual server configuration. Usually be found in /etc/nginx/site-available/.
location / {
return 301 https://www.YOURWEBSITE.com$request_uri;
try_files $uri $uri/ /index.php?$args;
}
For exception management, have a look at exceptions for redirects