The 53-year-old had been in a coma for a week after crashing her car into a house in Los Angeles.
"Today we lost a bright light, a kind and most joyful soul", her family said in a statement on Friday.
Heche appeared in films including Volcano, Donnie Brasco and the 1998 remake of Psycho.
The mother-of-two also appeared on Dancing with the Stars, the US equivalent of Strictly Come Dancing, in 2020.
