The late 'I Will Always Love You' singer's daughter announced she had secretly married her fiancé earlier this month, and says her mother - who died of accidental drowning in 2012 - would have supported the union, even though Nick was raised as her stepbrother.
Speaking on US TV's 'Extra', Bobbi, 20, said: ''She wanted this. This is something she wanted to see.''
Nick added: ''[Whitney] just treated me like she gave birth to me. She treated me like a son. She made me promise several times to look after Krissy ... and Mom, I will never, ever, ever break that promise.''
Nick, now in his 20s, was taken in by Whitney when his mother could no longer care for him, before he was a teenager. He was never officially adopted by the star and he and Bobbi - whose father is singer Bobby Brown - have no blood relatives.
Nick explained: ''Me calling [Whitney] mom, this where everybody gets the ['brother and sister' thing from].
''We were young. Krissy looked at me as an older brother, and I looked at her as a little sister.''
Romance between the pair blossomed after Whitney's death, and the couple claim negative reaction to their relationship only made them stronger.
Bobbi Kristina said: ''It lit a fire up under our ass and we went hauling.'' Nick added: ''The critics can say whatever they want to say ... it's like we have a force field and that s**t's just bouncing off of it.''