The PHP constants below will disable the default WordPress emails on WordPress, themes and plugin updates. They should be added into your wp-config.php file.
// Disable WordPress core update emails add_filter( 'auto_core_update_send_email', '__return_false' ); // Disable WordPress plugin update emails add_filter( 'auto_plugin_update_send_email', '__return_false' ); // Disable WordPress theme update emails add_filter( 'auto_theme_update_send_email', '__return_false' );