Fisher was taken ill on a flight from London to LA on Friday and was taken to hospital when the plane landed.
But a family statement said with "deep sadness" she died on Tuesday morning.
As well as starring in other films such as The Blues Brothers and When Harry Met Sally, Fisher also wrote four novels and three memoirs.
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 this morning.
"She was loved by the world and she will be missed profoundly. Our entire family thanks you for your thoughts and prayers."
The daughter of singer Eddie Fisher and actress Debbie Reynolds, Carrie Fisher made her film debut opposite Warren Beatty in 1975's Shampoo.
But far greater fame was to follow when she played Princess Leia in the original Star Wars trilogy, a role she reprised in last year's reboot The Force Awakens.
She endured a difficult private life, and has often discussed her years of mental illness and drug addiction.
More to come