After colliding with a residence in Los Angeles, the 53-year-old had been in a coma for one week.
Her family wrote in a statement on Friday, "Today we lost a bright light, a kind, and most joyful soul."
Heche's filmography includes Volcano, Donnie Brasco, and the 1998 adaptation of Psycho.
In 2020, the mother of two also appeared on the American edition of Strictly Come Dancing, Dancing with the Stars.
According to the Los Angeles Fire Department (LAFD), Heche's vehicle "erupted in heavy fire," which 59 firemen extinguished in more than an hour. The two-story house she collided into was rendered uninhabitable.
In addition to suffering burns, the actress was diagnosed with "a severe anoxic brain injury," which occurs when the brain is deprived of oxygen, according to her relatives.
A spokesman stated that the late actress is "legally dead." Still, he added that her life-support treatment would continue briefly to determine if she is a possible organ donor.
"Anne will be deeply missed, but she lives on through her beautiful sons, her iconic body of work, and her passionate advocacy," her family said in a statement.
Her courage in always speaking her truth and spreading her message of love and acceptance will have a lasting influence.
Heche was born in Ohio in 1969, and her family frequently relocated throughout her childhood.
Her father died of HIV/Aids when she was 13 years old, and she revealed in her 2001 memoir Call Me Crazy that he had regularly raped her as a youngster.
In interviews advertising the book, she stated that the abuse rendered her "insane" for the first 31 years of her life and that she developed the "Fourth Dimension" to feel safe.
Three months after her father's death, her brother was believed to have committed suicide in a car accident. Her mother refuted the suicide and abuse allegations, and the two became estranged.
After her family moved to Chicago, a talent agency discovered Heche in a school play.
In the late 1980s, she became well-known for portraying the identical twins Vicky Hudson and Marley Love in the serial opera Another World. She received a Daytime Emmy Award and two Soap Opera Digest Awards for her roles.
In the late 1990s, Heche rose to notoriety for her role as Maggie in the crime drama film Donnie Brasco, opposite Johnny Depp. She later told reporter Larry King that working with Depp was "heaven."
She played Amy Barnes, a geologist, and seismologist, opposite Tommy Lee Jones in the catastrophe film Volcano and Melissa "Missy" Egan in the cult horror film I Know What You Did Last Summer.
Before portraying Marion Crane in Gus Van Sant's version of the iconic horror film Psycho, she acted in the action-comedy picture Six Days, Seven Nights, and the drama-thriller Return to Paradise.
Before 1997, she had exclusively dated men; she began dating US talk show presenter and comedian Ellen DeGeneres in 1997. The prominent couple indicated they would obtain a civil union in Vermont if the option became available, but they separated three years later.
Heche reportedly struggled with mental health issues and substance abuse and was hospitalized at one time after parking on a California freeway and heading into the desert.
In 2001, Heche wed "Coley" Laffoon, a videographer she met during Ellen DeGeneres' stand-up tour, and the couple had a son before separating over six years later. She supposedly left her spouse for her co-star in Men in Trees, James Tupper, and her representative confirmed in 2008 that she was pregnant with her second son. The pair separated in 2018.
The new millennium heralded a shift in career direction, with appearances in fewer blockbusters and more praised independent films, such as the drama Birth, the sex comedy Spread, and 2011's Cedar Rapids, about a naive insurance agent on a life-altering business trip to Iowa.
She was nominated for an Emmy for her performance as Roweena Lawson in the 2004 television film Gracie's Choice, in which a teenage girl struggles to raise her brothers when their drug-addicted mother is sent to prison.
The same year, she was nominated for best actress at the Tony Awards for her performance in Twentieth Century opposite Alec Baldwin on Broadway.