What do you say to POIs when you accept the offer from their school?

[Pomegranateseed15]

Is it common to contact professors you've been in communication with to let them know that you're accepting their school's offer?

Is it usually just a brief FYI type email or longer/introductory? 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?

[DRMF]

That looks good to me.