What do you say to a professor/potential advisor when you accept the offer from their school? Is it common to contact professors you've been in communication with to let them know that you're accepting their school's offer? Do you usually contact the professors that met with you on a campus visit? 

Is it usually just a brief FYI type email or a longer/introductory letter? I've already visited campus and spoken to my potential supervisors/advisors.

How does this sound?


  Dear Professor L,
  
  I hope all is well. I'm writing to let you know I've accepted School's
  offer for the PhD program. I am grateful for this opportunity and I
  look forward to working with you and the rest of the faculty in X
  Subfield! 
  
  Best regards,
  
  Pomegranateseed15


Anything I should add?
Your suggestion is good. I don't think it needs more. One option, though, would be an additional sentence asking if there are any papers or sources that you can or should examine in the short term. 

But thanks is all you really need.