She was taken ill on a flight from London to Los Angeles on Friday and was taken to hospital when the plane landed.
A family statement announced she had died on Tuesday morning.
Tributes have been pouring in, with Star Wars co-star Mark Hamill simply tweeting: “No words #devastated”.
In a statement released on behalf of Fisher’s daughter Billie Lourd, 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 (16:55 GMT) this morning.
“She was loved by the world and she will be missed profoundly. Our entire family thanks you for your thoughts and prayers.”
Her mother, the actress Debbie Reynolds, wrote on her Facebook page: “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.”
Star Wars co-star Harrison Ford described Fisher as “one-of-a-kind” who lived her life “bravely”.
Series creator George Lucas said she was “extremely smart; a talented actress, writer and comedienne with a very colourful personality that everyone loved”.
“She has inspired me by teaching me that just because you’re a little broken or a little different you can still be an inspiration and shine like she did. She was honest about her health issues and was just herself.
“She taught me to not feel embarrassed or a lesser person just because you sometimes struggle to get through the day. Her death has hit me hard but it also makes me feel so proud to have been like her, different.”
Fisher had been on tour promoting her latest book, The Princess Diarist, when she was taken ill in the later stages of the flight to Los Angeles. A medic who was travelling on the plane administered first aid before it landed.
The daughter of singer Eddie Fisher and Debbie Reynolds, Carrie Fisher made her film debut opposite Warren Beatty in 1975’s Shampoo.
She also appeared in The Blues Brothers, When Harry Met Sally and Hannah and Her Sisters, and provided the voice of Peter Griffin’s boss Angela in the adult animated sitcom Family Guy.
But her enduring fame is thanks to her role as Princess Leia in the original Star Wars trilogy, a part she reprised in last year’s reboot The Force Awakens.
Discussing the part, she told the Daily Mail in 2011 that when she got the role in a “little science-fiction film”, she just thought of it as a bit of fun.
“It exploded across the firmament of pop culture, taking all of us along with it. It tricked me into becoming a star all on my own.”
She was also a successful writer, publishing several novels and memoirs, and working on the scripts for films like The Wedding Singer and Sister Act.
Her latest memoir, The Princess Diarist, contained revelations of an affair with Harrison Ford while the pair were shooting the first Star Wars film in 1976.
Fisher endured a difficult private life, and discussed her years of mental illness and drug addiction in interviews and writing. An early memoir was called Wishful Drinking.
The entertainment world has been quick to mourn and celebrate her life.