I agree strongly with Cherryblossom here. It's up to you what, how much and when you share information about your past, and that includes with your partner, your therapist and everyone else. Yes, there is a point at which I believe it is incredibly important and healing to share with safe and supportive people in your life and this allows them to give you the support and understanding that will further aid your healing.
But timing, and feeling safe and ready in the relationship, is critical, and telling too much before you're ready can be a very destabilising experience for you that would not benefit either you or your relationship.
I do totally understand shame - gosh, believe me I do, and it's hard when shame is part of what holds you back. But shame in itself is something to be worked through, with your therapist in particular, and dealing with that shame so that you can manage it is a critical foundation to work on before you begin to share the things for which you are ashamed.
I say all that to say... try not to put pressure on yourself about what you should do. Being in a committed relationship doesn't mean telling the other person everything just on principle - and that goes for everyone. If he truly does love and support you as you say, he will trust your judgment, and respect your healing, and be there to walk all the steps of this journey with you, even the ones that come before being able to talk about the past.
Maddog