I'm inclined to agree with Ian. I never actually reached the "normal" range on the BMI charts for my height. But I consider myself a formerly-fat person and I say things like "when I was fat...."
It is not a technical designation or a medical one, but a mental one. It's how I feel. I feel so radically different from how I did in my old body - in strength, stamina, desire to move.
And as a matter of course I eat differently from how I did when I was fat. Even though I sometimes slip up, return to binging behaviors, and have partial regains, getting back on plan now feels like getting my eating back to my normal state, rather than getting back on a diet.
It took several years of hard work but the changes I made in my life and my body have become the new normal for me. And along with that, gradually, came thinking of myself as no longer fat. It wasn't crossing a numerical threshold that did it for me.