Here is a small plugin I made to allow you to do exactly this, it also works on multiple background images and multiple elements:
Read the article:
http://catmull.uk/code-lab/background-image-loaded/
or go straight to the plugin code:
http://catmull.uk/downloads/bg-loaded/bg-loaded.js
So just include the plugin and then call it on the element:
<script type="text/javascript" src="http://catmull.uk/downloads/bg-loaded/bg-loaded.js"></script>
<script type="text/javascript">
$('body').bgLoaded();
</script>
Obviously download the plugin and store it on your own hosting.
By default it adds an additional "bg-loaded" class to each matched element once the background is loaded but you can easily change that by passing it a different function like this:
<script type="text/javascript" src="http://catmull.uk/downloads/bg-loaded/bg-loaded.js"></script>
<script type="text/javascript">
$('body').bgLoaded({
afterLoaded : function() {
alert('Background image done loading');
}
});
</script>
Here is a codepen demonstrating it working.