Scacchi was born on 18 February 1960 in Milan, Italy, the daughter of Luca Scacchi, an Italian art dealer and painter, and Pamela Risbey, an English dancer and antiques dealer. Scacchi's parents divorced when she was four, and her mother returned to her native England with Greta and her two older brothers, first to London, then to Haywards Heath, West Sussex.
In 1975, after her mother's remarriage, the family moved to Perth, Western Australia, where her stepfather was a visiting professor at the University of Western Australia (UWA). While in Perth, Scacchi attended Hollywood Senior High School and joined UWA's University Dramatic Society, where she made her theatrical debut at the New Dolphin Theatre in Edward Bond's play Early Morning under director Arne Neeme.
