Britton was born Constance Elaine Womack in Boston, Massachusetts, to Linda Jane (née Cochran) and Edgar Allen Womack, Jr., who was a physicist and an energy company executive. She spent her early years in Rockville, Maryland. When she was seven years old, she moved with her parents and her fraternal twin sister, Cynthia, to Lynchburg, Virginia, where she attended E.C. Glass High School. She majored in Asian studies with a concentration in Chinese at Dartmouth College, and studied at the Beijing Normal University in Beijing during her freshman summer with Kirsten Gillibrand, now a U.S. Senator from New York. After graduating in 1989, she moved to New York City, where she spent two years at the Neighborhood Playhouse School of the Theatre studying with Sanford Meisner.
Britton received accolades for her starring roles in Edward Burns' acclaimed independent films The Brothers McMullen (1995) and No Looking Back (1998). In the former, she captivated moviegoers with her portrayal of "Molly", the luminous wife of a cheating husband. This popular low-budget film went on to win the Grand Jury Prize at the Sundance Film Festival. After nearly canceling her audition with director Edward Burns, this last meeting of the day turned into the role that would launch her career. Born in Boston, Massachusetts, Britton moved to Lynchburg, Virginia, at the age of seven with her family, including her fraternal twin sister. She went on to attend Dartmouth College, where she majored in Asian studies and spent a term in Beijing, China. Upon graduation, she moved to New York, where she spent two years at the Neighborhood Playhouse studying with Sanford Meisner, and an additional two years performing in regional theater and off-Broadway productions. She moved to Los Angeles after the success of The Brothers McMullen (1995). She starred in ABC's Lost at Home (2003) opposite Mitch Rouse and Gregory Hines. Her other television credits include The Fighting Fitzgeralds (2001) opposite Brian Dennehy, a recurring role in the highly-acclaimed drama The West Wing (1999) and a starring role in the award-winning comedy Spin City (1996) opposite Michael J. Fox. Additionally, Britton starred in the recent feature films The Next Big Thing (2001) and One Eyed King (2001). In her free time, Britton, who resides in both New York and Los Angeles, enjoys hiking, yoga, and doing volunteer work.