Bobbi, 20, shared the happy news on Twitter on Thursday, writing: "#HappilyMarried So #Inlove if you didn't get it the first time that is."
The young beauty accompanied the message with a snap of her and Nick's hands – hers placed tenderly over his – showing off his wedding band and her dazzling wedding ring.
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The daughter of the late superstar and Nick announced their engagement in October 2012, during her family's short-lived reality series The Houstons: On Our Own.
But their unconventional love was met by widespread disapproval as legendary singer Whitney informally adopted Nick at the age of 12, when he went to live with the mother and daughter.
Bobbi was forced to defend the relationship at the time, taking to Facebook to set the record straight.
"YES, we me 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.'
"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 she knew that we were going to start dating."
While the pair have had an on-off relationship – they split shortly after the show and got back together in July – they appear committed.
Last September, Nick shared on Twitter that he had upgraded Bobbi's custom-made Neil Lane sparkler by adding two extra bands.