Britton was born Constance Womack in Boston, Massachusetts, the daughter of Linda and Allen Womack, who was a physicist.When she was seven years old, her family (mother Linda, father Allen, and sister Cynthia) moved to Lynchburg, Virginia. She majored in Asian Studies at Dartmouth College (class of 1989). Upon graduation she moved to New York City, where she spent two years at the Neighborhood Playhouse studying with Sanford Meisner. Britton uses her married name as her stage name, though she is now divorced from her husband.