When you are offered a promotion at your job there are several ways to say "Thank you" to your boss appropriately. It is most appropriate to say a simple "Thank you" when you are offered the job and then later to write a note.
When you are first offered the promotion make sure you say "Thank you," but do not gush. Simply state that you will work hard to make sure the work you are promoted to do is successful. After you start your new job, make sure to write a nice thank you note to your boss. In the note state that you have worked hard for this position and that you are thankful for the opportunity.