UsMagazine.com said Houston informally adopted Gordon when he was 12 years old and referred to him as her "son" prior to her February 2012 death.
Brown and Gordon were previously engaged, but called it off in November 2012 due to pressure from Brown's disapproving family, the celebrity news website said.
However, Brown went online Wednesday to announce she and Gordon are once again planning to wed.
"Yes, me and Nick are engaged. I'm tired of hearing people say, 'Eww you're engaged to your brother' or 'If Whitney was still alive, would we be together or would she approve of this?'" the 20-year-old daughter of singer Bobby Brown wrote on Facebook.
"Let me clear up something, we aren't even real brother and sister, nor is he my adoptive brother. My mom never adopted him. In fact, mommy was the one who even said that she knew that we were going to start dating," she added. "My mom knows me better than any of you. A lot of y'all are saying that y'all are only saying this all out of love. Which is bull because if that was so, all you would want is for me to be happy. People need to seriously stop judging my relationship. Pretty sure it's my own decision who I want to be with. Yes, my relationship may not be perfect. We will have rough patches, just like every other relationship. And we have had our rough patches. You may or may not agree with my relationship. You may or may not respect it. Judge me, go ahead. Your opinions are yours and mine are mine. It is my life and not yours. The decisions I make have nothing to do with you."