This is a very brave thing for you to do, and I understand how hard it is.
My parents and I are close and always have been, but I also had the worries and fears about their reactions.
Technically, the first time I told them was when I was inpatient and 18 years old - just told them the barest of basics over the phone.
When it became necessary to tell them more of the who and the what, it was a couple of years later. I wrote a note and put it on top of my mother's purse, asking her not to read it until I was gone for the day. Then I received an email from her saying she would respect any space I needed and that she and Dad would follow my lead when I got back home. Of course, they had to grapple with their own emotions when it came to this, which I knew, and some family therapy sessions helped. The day I wrote the letter, I had therapy, so I knew I'd be able to process it there.
I hope your parents react well and respect your wishes to not go into detail.
Keep talking to us here while you go through this difficult time, we're here for you.