This may sound strange, but I think you need to have a medical evaluation to see if your child IS really a boy. I have heard of children being born with BOTH sets of genitals, but since the male genitalia was visible, everyone just assumed the child was male, but it was actually female when you looked at chromosomes. The child also had a uterus and ovaries. After having been raised as a boy, the person started living as a woman when she got old enough to chose her own way. She had the penis removed surgically, and lived happily ever after as they say. If the child is insisting he is a girl, and has always been this way, I would definitely have it checked out!
You are adopting a sensible and understanding approach to your son, and he does require the sort of sensitive management that you are displaying. It would be wise to seek the involvement of a pediatric mental health clinician, who can help to flesh out your son's perceptions about gender-related matters. One of the keys is to determine if, as a male, he experiences overt disadvantages (from his perspective) to being male and, in a similar vein, overt advantages to being female. The clinician can also offer you some ongoing advice about how to manage this difficult situation as a parent.