The 69-year-old businessman was in the USA at the time.
Star Wars Icon Carrie Fisher Dies Aged 60
The famed Star Wars actress passed away aged 60 four days after suffering a heart attack.
The legendary American actress died in hospital where she had been receiving treatment after becoming unwell on the flight from London.
A statement from family spokesman Simon Halls said: "It is with a very deep sadness that Billie Lourd confirms that her beloved mother Carrie Fisher passed away at 8.55 this morning."
Ms Lourd added that her mother was "loved by the word and she will be missed profoundly".
She is survived by her brother, Todd Fisher, and her mother actress Debbie Reynolds.
Fisher made a much welcomed return to the Star Wars franchise in 2015.
News first surfaced of the star's condition on TMZ after passengers attempted to revive Fisher with CPR. The mother-of-one was then rushed to hospital when the plane landed after midday local time (20:00 GMT).
Fisher, aged 60, first stole our hearts in 1977 as the Princess of the planet Alderaan and an agent of the rebel alliance in the original Star Wars movie.
Despite being best known for her role as Princess Leia, Carrie Fisher also had a successful acting career in films such as 'Shampoo', 'When Harry Met Sally' and 'The Blues Brothers' as well as cameos in 'Austin Powers: International Man Of Mystery', 'Scream 3' and 'Charlie's Angels: Full Throttle'.
Fisher was best known for her role as Princess Leia in the Star Wars franchise.
The movie icon was also on tour promoting her latest book, 'The Princess Diarist' - a tell all memoir that revealed what happened behind-the-scenes of one of the world's biggest movie sets.
Her openness about addiction and being diagnosed with bipolar disorder, made Fisher an advocate for mental health, winning her an Outstanding Lifetime Achievement Award in Cultural Humanism, noting that "her forthright activism and outspokenness about addiction, mental illness, and agnosticism have advanced public discourse on these issues with creativity and empathy.".
The news comes after fans took to social media with encouraging memes and posts, pushing for the actresses's recovery using the 'cinnamon bun' hairstyle heroin as their muse.
Dear 2016: This is not the princess you are looking for. Move along. Move along. #carriefisher— Paul Bennett (@BennettWriting) December 23, 2016
Among the well wishers was actor Matt Lanter who played the famous Anakin from the Star Wars movies, who also sent the 'force vibes' to be with her.
Sending fatherly Force vibes to #CarrieFisher ...I'm hoping to hear some positive news soon.— Matt Lanter (@MattLanter) December 24, 2016
He didn't just say that, did he?