Redirect a user once they have signed up and paid for a site

A couple of my customers have complained to me that the sign-up process for a new site is a little bit confusing, I actually had one client accidentally pay twice! The general feeling is that once a user has paid, it's kind of confusing to go back to their account page - I think it would be better to redirect to a different page, or better still, straight to the dashboard so users can start building their site right away.

Is there a way to set up a redirect once a site has been created and payment has been successful?