The American star - who is best known for her role in the 50s cult classic movie `Forbidden Planet` - was diagnosed with lung cancer in 2007 but died from complications of pancreatic cancer at a retirement home in Santa Barbara on Sunday (02.01.11) according to her daughter Jane Uemura.
Family spokeswoman Melissa Fitch added family and friends were with the veteran actress when she died.
Along with a film career, Anne also enjoyed success on the small screen where she played the title role in `Honey West` the mid 1960s TV series about a female private detective with a pet ocelot.
She was nominated for an Emmy and won a Golden Globe for the role.
The actress - real name Ann Marvak - was born in New York in 1930 and worked as a child model before appearing on Broadway in some small roles.
She began her movie career at MGM in 1947 and went on to act opposite stars such as Spencer Tracy, James Cagney and Jerry Lewis.
Anne was married twice - to the actor and director Bamlet L. Price Jr. and Dr. Robert Abeloff - with both ending in divorce.
She is survived by her daughters Jane and Maggie and a grandson.