She has appeared in over 40 films in her career. Notable roles include Jessica Bradford in the 1974 Canadian horror movie Black Christmas, Mary, the mother of Jesus in the 1977 Zeffirelli TV production of Jesus of Nazareth, and as Rosalie Otterbourne in Death on the Nile (1978) with Peter Ustinov. One of her other great performances was as Rebecca of York in the 1982 made for TV remake of Ivanhoe. She is known for her natural beauty, reportedly wearing little or no makeup in her roles.

Hussey was born in Buenos Aires, the daughter of Andreas Osuna (aka Isvaldo Ribo), an Argentinian opera and tango singer and his English wife Joy Hussey. Her mother took Olivia and her younger brother to live in England when she was seven years old, she then attended a Drama School for five years. Her first role was as Jenny in The Prime of Miss Jean Brodie with Vanessa Redgrave where Zeffirelli spotted her and chose her out of 500 other actresses for the role of Juliet in 1968.

Hussey was married first to actor Dean Paul Martin (son of the famous Rat Pack singer/actor, Dean Martin) from 1971 until 1978. They had a son, Alexander Dean Martin, in 1973. In 1980 she married Japanese musician Akira Fuse and bore one son, Maximillian Fuse. After their divorce in 1989 Hussey married a third time to David Glen Eisley, an American musician. Together they had Hussey's third child, daughter India Joy Eisley.

In 2003, Hussey played the lead in a film adaptation on the life of Mother Teresa.