You should specify what kind of element is IDOFELEMENT. But you can't convert it to a link by just adding a href attribute, it only works if IDOFELEMENT
is an hyperlink like <a id="IDOFELEMENT">stuff</a>
Simplest way is to add an onclick event to the element that changes the url to desired address:
<script type="text/javascript">
   var element = document.getElementById("IDOFELEMENT");
   element.setAttribute('onclick', 'window.location.href=\'http://address.com\'');
</script>
Or if you wanna wrap it with a hyperlink:
<script type="text/javascript">
   var element = document.getElementById("IDOFELEMENT");
   var parent = element.parentNode; 
   var link = document.createElement('a');
   link.href = 'http://www.address.com';
   link.appendChild(element.cloneNode(true)); 
   parent.replaceChild(link, element);
</script>
I hope this helps you.