There is a Timeline.Completed Event that you can use. You can either set it in XAML, or in C# on a Storyboard instance. The linked page has a full working example that you can view.
The handler used is the default EventHandler delegate:
private void StoryboardCompleted(object sender, EventArgs e)
{
// the Storyboard has stopped
}
UPDATE >>>
Although the Completed event can be set on a Storyboard instance, it is in fact defined in the Timeline class. As Timeline is the base class for all AnimationTimeline classes, this means that you can also attach a handler to the Completed event from the AnimationTimeline object that you are passing into the BeginAnimation event.