The British star, who had been suffering from lung cancer for some time, passed away at her home in Santa Monica, California on Friday (22Jan10), a week before her 81st birthday, according to her agent.
Simmons rose to fame playing Estella in 1946 movie Great Expectations, she then went on to secure a string of leading Hollywood parts, including a role in Laurence Olivier's 1948 film Hamlet, for which she gained an Oscar nomination for her portrayal of Ophelia. She received a second Oscar nod for 1969's Happy Ending.
Simmons is also known for appearing opposite Marlon Brando in 1955's Guys and Dolls, and Kirk Douglas in 1960's Spartacus.
The legendary actress married twice - once to British actor Stewart Granger, who she met while filming Cleopatra, before divorcing after ten years in 1960. The pair had one daughter, Tracy, together.
She then went on to marry director Richard Brooks the same year (60). They also had a daughter, Kate, but the couple divorced in 1977.