Britton was born Constance Elaine Womack to Edgar Allen Womack, Jr. and Linda Jane (nee Cochran). Her father, Edgar, was a physicist and energy company executive. Britton has a fraternal twin sister named Cynthia. Britton was born in Massachusetts but grew up in Rockville, Maryland. Her family moved to Lynchburg, Virginia when Britton was seven years old. She attended E.C. Glass High School where she preformed in plays in the drama club. After graduating high school, she attended Dartmouth College where she majored in Asian Studies with a concentration on Chinese. After graduating from Dartmouth in 1989, Britton moved to New York City. She met her now ex husband John Britton at a Greek house gathering at Dartmouth College. She adopted a child from Ethiopia named Eyob "Yoby" Britton in 2011. When she got the part of Rayna Jaymes in the television show, Nashville, Britton moved to Nashville, Tennessee.
- Attended Beijing Normal University in Beijing, China with Kirsten Gillibrand, who is now a US Senator
- Even though she's been divorced since 1995, Connie still uses her married name as her stage name