Aniston was born in Sherman Oaks, California, the daughter of actor John Aniston and actress Nancy Dow (1936–2016). Her father is Greek, while her mother was born in Connecticut. One of her maternal great-grandfathers was an Italian immigrant, and her mother's other ancestry includes English, Irish, Scottish, and a small amount of Greek. Aniston has two half-brothers, John Melick, her older maternal half-brother, and Alex Aniston, her younger paternal half-brother. Aniston's godfather was actor Telly Savalas, one of her father's best friends.
As a child, Aniston moved to New York City. Despite her father's television career, Aniston was discouraged from watching TV, though she found ways around the prohibition. When she was six, she began attending a Waldorf school. Her mother and father split up when she was nine years old. Her father is best known for his role as Victor Kiriakis on the NBC daytime drama Days of Our Lives, which he originated in 1985. Her mother appeared in two 1960s TV series, The Wild Wild West and The Beverly Hillbillies.
Having discovered acting at age 11 at the Waldorf school, Aniston enrolled in and graduated from Manhattan's Fiorello H. LaGuardia High School of Music & Art and Performing Arts, where she joined the school's drama society. Anthony Abeson was her drama teacher. She was in The Sign in Sidney Brustein's Window by Lorraine Hansberry and Three Sisters by Anton Chekhov.