Watts was born 28 September 1968, in Shoreham, Kent, England. She is the daughter of Myfanwy ("Miv") Edwards (née Roberts), an antiques dealer and costume and set designer, and Peter Watts (1946–1976), a road manager and sound engineer who worked with Pink Floyd. Miv was born in England but lived in Australia between the ages of one and seven. Watts' maternal grandfather was Welsh and her maternal grandmother was Australian.
Watts' parents divorced when she was four years old. After the divorce, Watts and her elder brother, Ben Watts, moved several times across South East England with their mother. Peter Watts left Pink Floyd in 1974, and he and Myfanwy were later reconciled. Two years later, in August 1976, he was found dead in a flat in Notting Hill, of an apparent heroin overdose.
Following his death, Watts' mother moved the family to Llanfawr Farm in Llangefni and Llanfairpwllgwyngyll, towns on the island of Anglesey in North Wales, where they lived with Watts' maternal grandparents, Nikki and Hugh Roberts, for three years. During this time, Watts attended a Welsh language school, Ysgol Gyfun Llangefni. She later said of her time in Wales: "We took Welsh lessons in a school in the middle of nowhere while everyone else was taking English. Wherever we moved, I would adapt and pick up the regional accent. It's obviously significant now, me being an actress. Anyway, there was quite a lot of sadness in my childhood, but no lack of love." In 1978, her mother remarried (though she would later be divorced again) and Watts and her brother then moved to Suffolk, where she attended Thomas Mills High School. Watts has stated that she wanted to become an actress after seeing her mother performing on stage and from the time she watched the 1980 film Fame.
In 1982, when Watts was 14, she moved to Sydney, New South Wales in Australia with her mother, brother and stepfather. Myfanwy established a career in the burgeoning film business, working as a stylist for television commercials, then turning to costume design, ultimately working for the soap opera Return to Eden. After emigrating, Watts was enrolled in acting lessons by her mother; she auditioned for numerous television advertisements, where she met and befriended actress Nicole Kidman. Watts obtained her first role in the 1986 drama film, For Love Alone, based on the novel of the same name by Christina Stead, and produced by Margaret Fink.
In Australia, Watts attended Mosman High School and North Sydney Girls High School. She failed to graduate from school, afterwards working as a papergirl, a negative cutter and managing a Delicacies store in Sydney's affluent North Shore.
She decided to become a model when she was 18. She signed with a models agency that sent her to Japan, but after several failed auditions, she returned to Sydney. There, she was hired to work in advertising for a department store, that exposed her to the attention of Follow Me, a magazine which hired her as an assistant fashion editor. A casual invitation to participate in a drama workshop inspired Watts to quit her job and to pursue her acting ambitions.
Regarding her nationality, Watts has stated: "I consider myself British and have very happy memories of the UK. I spent the first 14 years of my life in England and Wales and never wanted to leave. When I was in Australia I went back to England a lot." She also has expressed her ties to Australia, declaring: "I consider myself very connected to Australia, in fact when people say where is home, I say Australia, because those are my most powerful memories."