I just wanted to add this version because this is such a useful thread and I think this is a very simple implementation. I have used this multiple times in various types if multithreaded application:
Task.Factory.StartNew(() =>
{
DoLongRunningWork();
Application.Current.Dispatcher.BeginInvoke(DispatcherPriority.Normal, new Action(() =>
{ txt.Text = "Complete"; }));
});