Kristen Foster said she passed away on Sunday surrounded by her family and was "finally at peace in the arms of God".
Brown was discovered face down and unresponsive in a bathtub on 31 January and placed in a medically induced coma. She never regained consciousness.
She was moved to a hospice in the city of Duluth, Georgia, a month ago after her condition deteriorated.
Brown was the only daughter of Houston and R&B singer Bobby Brown.
Whitney Houston was found dead in a hotel bath in Los Angeles in 2012.
The family posted a photo of Whitney with Bobbi Kristina as a baby on whitneyhouston.com with the following message:
"It is hard to say goodbye. On Sunday, July 26, Bobbi Kristina Brown made her transition peacefully. The family thanks everyone for their loving thoughts and prayers. As Bobbi Kristina would say: 'The wind is behind me and the sun is in my face.'"
"Bobbi Kristina Brown passed away July 26 2015, surrounded by her family," Ms Foster added.
"She is finally at peace in the arms of God. We want to again thank everyone for their tremendous amount of love and support during these last few months."
Singer Dionne Warwick, Whitney Houston's cousin, described Bobbi Kristina as "a sweetheart".
"She will be missed, that's for sure. She was a good girl. She was a good little girl. She really was," she told Bravo's Watch What Happens Live.
Other stars paid tribute on Twitter, including Selma director Ava DuVernay, who said: "She seemed to be caught in the web of celebrity upon arrival. Twenty two years. A sad end. May the sister have peace now."
The BBC's Regan Morris in Los Angeles says Brown had dreamed of carrying on her mother's legacy as a singer and actress, and had a few small TV roles - but her career had not yet taken off.
In January, police said Brown was found face down in a bathtub in the suburban Atlanta home she shared with Nick Gordon, the man she called her husband. A police report described the incident as a "drowning".
Mr Gordon said at the time she did not appear to be breathing and lacked a pulse before emergency services arrived.
Brown was placed in a medically-induced coma and has been breathing with the aid of a ventilator.