Upgrade to Apache 2.4 requires new authorization configuration

I've done several updates on servers where Apache get's upgraded to 2.4 and I start getting "Forbidden" errors in the web browser. In short, the configuration parameters have changed from

<Directory /path/to/www/files>
    #...
    Order allow,deny
    Allow from all
   #...
</Directory>

to

<Directory /path/to/www/files>
    #...
    Require all granted
    #...
</Directory>

More information here.