Klettseb's solution should work, but I'd recommend a lighter approach instead of overriding the entire Subscriber class:
\app\etc\modules\Yourcompany_Newsletter.xml
<?xml version="1.0"?>
<config>
<modules>
<Yourcompany_Newsletter>
<active>true</active>
<codePool>local</codePool>
<version>1.0.0</version>
</Yourcompany_Newsletter>
</modules>
</config>
\app\code\local\Yourcompany\Newsletter\etc\config.xml
<?xml version="1.0" encoding="UTF-8"?>
<config>
<modules>
<Yourcompany_Newsletter>
<version>1.0.0</version>
</Yourcompany_Newsletter>
</modules>
<global>
<models>
<yourcompany_newsletter>
<class>Yourcompany_Newsletter_Model</class>
</yourcompany_newsletter>
<newsletter>
<rewrite>
<subscriber>Yourcompany_Newsletter_Model_Subscriber</subscriber>
</rewrite>
</newsletter>
</models>
</global>
</config>
\app\code\local\Yourcompany\Newsletter\Model\Subscriber.php
<?php
class Yourcompany_Newsletter_Model_Subscriber extends Mage_Newsletter_Model_Subscriber
{
/**
* send the confirmation-success email if newsletter subscription is confirmed
*/
public function confirm($code)
{
$isConfirmed = parent::confirm($code);
if ($isConfirmed == true) {
$this->sendConfirmationSuccessEmail();
}
return $isConfirmed;
}
}