Connelly was born in the Catskill Mountains, New York, the daughter of Eileen, an antiques dealer, and Gerard Connelly, a clothing manufacturer who worked in the garment industry. Connelly's paternal grandparents were of Irish and Norwegian descent, respectively, while her maternal grandparents were Jewish, their families having come from Russia and Poland. Connelly was raised in Brooklyn Heights, near the Brooklyn Bridge, and attended St. Ann's School, except for four years the family spent living in Woodstock, New York. One of her father's friends was an advertising executive, who suggested that she audition at a modeling agency.

At the age of ten, her career started in newspaper and magazine ads, then moved to television commercials. These led to movie auditions and her first film role was as "young Deborah Gelly", a supporting role in Sergio Leone's 1984 gangster epic, Once Upon a Time in America, filmed mostly in 1982 when she was eleven. She next starred in Italian horro