Close was born in Staten Island, New York. Close's father is an orthopedic surgeon. Close is the eldest of three brothers. His family moved to Indiana, then to Michigan, and finally settled in San Diego when Close was seven years old.
Close graduated with a B.A. in Communications at the University of Southern California in 1989.
Close was interested in acting from an early age and had some stage experience in school, but did not decide to pursue an acting career until after college. His first role was in a theater production Rat Songs in L.A., after which he was offered a part in the film American Me (1992) and Safe House directed by Elena Mannus. He had a brief stint in daytime television when he played Sawyer Walker on NBC's daytime soap Santa Barbara from 1992 to 1993. He received a Soap Opera Digest Award nomination for Outstanding Male Newcomer for his role as Sawyer Walker on Santa Barbara. Close later had leading roles on short-lived primetime shows such as McKenna (1994–1995), Dark Skies (1996–1997), The Magnificent Seven (1998–1999), Now and Again (1999–2000), and the Steven Spielberg produced miniseries Taken (2002).
Close is best known for his role on CBS drama Without a Trace as FBI agent Martin Fitzgerald. The show ran for seven seasons from 2002 to 2009. He later had recurring role on Suits, and was series regular on another CBS show Chaos. In 2012, Close began co-starring with Connie Britton in the ABC drama Nashville as Teddy Conrad, initially the husband of Britton’s character Rayna Jaymes and later the mayor of Nashville.
Close married his wife Keri in 1995. They have two daughters Katie (born October 1998) and Ella (born April 2001). They are members of the Brentwood Presbyterian Church.