Campbell was born in Guelph, Ontario. Her father, Gerry Campbell, is an immigrant from Glasgow, Scotland, and works as a high school drama teacher at Erindale Secondary School in Mississauga, Ontario. Her mother, Marnie Neve, is a psychiatrist of Sephardic Jewish descent from Amsterdam, the Netherlands. Campbell's maternal grandparents ran a theatre company in the Netherlands and her paternal grandparents were also performers. Her name, "Neve", is a Sephardic Jewish surname and means "snow" in Italian and "oasis" in Hebrew and Arabic. Neve was raised a Catholic but also identifies as Jewish.
Campbell rose to wider fame after being cast as the lead character, Julia Salinger, in the teen drama series Party of Five; she played this character from 1994 to 2000. Campbell's first widely released film was 1996's The Craft. She subsequently appeared in the enormously successful Scream horror film trilogy, as well as Wild Things, Blues Brothers 2000, and Three to Tango. She was on People's "50 Most Beautiful People" list in 1998.