The American star, best known for her role as Princess Leia in the films, 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”.
Mark Hamill, who starred as Luke Skywalker in the franchise, tweeted a picture of himself alongside Fisher and wrote “no words #Devastated”.
Co-star Harrison Ford, 74, said in a statement: “Carrie was one-of-a-kind… brilliant, original. Funny and emotionally fearless.
“She lived her life, bravely.”
And Fisher’s mother, actress Debbie Reynolds, wrote on Facebook: “Thank you to everyone who has embraced the gifts and talents of my beloved and amazing daughter.
“I am grateful for your thoughts and prayers that are now guiding her to her next stop. Love Carrie’s Mother.”
The actress and author had been on a tour to promote her new book, The Princess Diarist, in the UK, and had also been shooting the third season of the sitcom Catastrophe.
Carrie Fisher, the actress who found fame as Princess Leia in Star Wars, has died at the age of 60
The actress suffered a heart attack on a flight to Los Angeles
She starred in Star Wars with Mark Hamill and Harrison Ford, playing Princess Leia
Although best known for her iconic Star Wars character, she was also a successful writer, publishing Postcards From The Edge in 1987
Pictured with Harrison Ford at Comic-Con 2015
She suffered a heart attack as she travelled back to the US just before Christmas.
Doctors and nurses on board the aircraft performed CPR and paramedics met the flight at Los Angeles international airport.
Fisher made her film debut opposite Warren Beatty in the 1975 hit Shampoo, and was also an author who detailed her struggled with drug addiction and mental illness in several best-selling books.
She also had roles in films including Austin Powers, The Blues Brothers and When Harry Met Sally.
The actress will appear in the next Star Wars instalment, with a larger role than in 2015’s The Force Awakens.
I’m deeply saddened at the news of Carrie’s passing. She was a dear friend, whom I greatly respected and admired. The force is dark today!
— Billy Dee Williams (@realbdw) December 27, 2016
Last month, Fisher revealed she had a three-month affair with her Star Wars co-star Harrison Ford 40 years ago.
She told People magazine the affair started and ended in 1976 during filming for the sci-fi films. Fisher was 19 and Ford was 33 at the time.
She is survived by her brother, Todd Fisher, and her mother actress Debbie Reynolds.