The suggestion by hjpotter92 does not work in safari! I have made a small adjustment to the script so it now works in Safari as well.
Only change made is resetting height to 0 on every load in order to enable some browsers to decrease height.
Add this to <head>
tag:
<script type="text/javascript">
function resizeIframe(obj){
obj.style.height = 0;
obj.style.height = obj.contentWindow.document.body.scrollHeight + 'px';
}
</script>
And add the following onload
attribute to your iframe, like so
<iframe onload='resizeIframe(this)'></iframe>