Anderson was born in Chicago, Illinois, the daughter of Rosemary Anderson (née Lane), a computer analyst, and Edward Anderson, who owned a film post-production company.Soon after her birth, her family moved to Puerto Rico for 15 months; she then lived for five years in Roseberry Gardens, Crouch End, and finally for 15 months in Albany Road, N4 in North London, so that her father could attend the London Film School. When Anderson was 11 years old, her family moved again, this time to Grand Rapids, Michigan. She attended Fountain Elementary and then City High-Middle School, a program for gifted students with a strong emphasis on the humanities; she graduated in 1986.
Anderson was interested in marine biology, but began acting her freshman year in high school productions, and later in community theater, and served as a student intern at the Grand Rapids Civic Theatre & School of Theatre Arts. She attended The Theatre School at DePaul University in Chicago (formerly the Goodman School of Drama), where she earned a Bachelor of Fine Arts in 1990. She also participated in the National Theatre of Great Britain's summer program at Cornell University.
Anderson moved to New York when she was 20 years old. To support herself when she started her career, Anderson worked as a waitress. She began her career in Alan Ayckbourn's play, Absent Friends at the Manhattan Theatre Club alongside Brenda Blethyn; she won the 1990–91 Theatre World "Newcomer" Award for her role. Her next theatrical role was in Christopher Hampton's The Philanthropist at the Long Wharf Theatre in New Haven, Connecticut.
Anderson has three children. She has a daughter with ex-husband Klotz, Piper Maru (for whom The X-Files episode, "Piper Maru", was named), born on September 25, 1994, in Vancouver, Canada. During Anderson's pregnancy, The X-Files creator, Chris Carter, created an alien abduction storyline that kept Anderson off-camera long enough for labor, delivery and a 10-day maternity leave. Carter was named Piper's godfather. In 2000, Piper had a small (and uncredited) appearance in her mother's movie The House of Mirth. Anderson also has two sons, Oscar (born November 1, 2006) and Felix (born October 15, 2008).
In 1996, Anderson was voted the "Sexiest Woman in the World" for FHM's 100 Sexiest Women poll. In 2008, she also placed 21st in FHM's All Time 100 Sexiest Hall of Fame.
Anderson provides philanthropic and charitable assistance in the support of finding a cure for neurofibromatosis (NF). She serves as NF, Inc.'s Honorary Spokesperson and is a Patron of the Neurofibromatosis Association (based in the UK). Her support stems from her brother being diagnosed with NF-1. She is also a member of the board of directors for Artists for a New South Africa and a campaigner for ACTSA: Action for Southern Africa. Furthermore, Anderson is an active member of PETA, and supports animal rights. She also supports tribal rights charity Survival International leading to her performance in a London stage fundraiser in early 2010. In late 2010, Anderson and other celebrities joined a campaign to boycott Botswana diamonds over the government's treatment of the Kalahari Bushmen.