In directory.xml
Change:

    <reference name="header">
         <block type="directory/currency" name="currency" as="currency_switcher" template="directory/currency.phtml"/>
    </reference>

to:

    <reference name="footer">
         <block type="directory/currency" name="currency" as="currency_switcher" template="directory/currency.phtml"/>
    </reference>

**EDIT:**

By Default Currency should show on footer, if you look at directory.xml line 39

    <reference name="footer">
                <block type="directory/currency" name="footer_currency" after="footer_store_language" template="directory/currency.phtml"/>
            </reference> 

if it is not showing in footer so you need to add:

    <?php echo $this->getChildHtml('footer_currency') ?>