Linney was born in New York City. Her mother, Ann Perse (née Leggett), is a nurse who worked at the Memorial Sloan-Kettering Cancer Center in New York City, and her father, Romulus Linney, is a well-known playwright and professor. Linney's paternal great-great-grandfather was Republican U.S. Congressman Romulus Zachariah Linney. She has a half-sister, Susan, from her father's second marriage. Linney graduated from the Northfield Mount Hermon School in 1982. She then attended Northwestern University before transferring to Brown University, where she graduated with a Bachelor of Arts in 1986. After attending Brown, Linney went on to study acting at the Juilliard School.

Linney married David Adkins in 1995. They divorced in 2000. As of 2007, she was engaged to Marc Schauer, a real estate agent in Telluride, Colorado.