Channing was born in New York City to Lester Napier Stockard and Mary Alice English, a wealthy couple. She is an alumna of The Madeira School and graduated in 1965 from Radcliffe College where she studied history and literature. Channing then decided to pursue an acting career, starting in the Boston theatrical community, but eventually working in New York and Los Angeles.

One of Channing's earliest roles was as The Number Painter's victim, in a series of segments on Sesame Street. After brief appearances in 1971's The Hospital and 1972's Up the Sandbox, she landed her first lead role in the acclaimed 1973 television movie The Girl Most Likely To.... In 1975, she starred alongside Warren Beatty and Jack Nicholson in Mike Nichols' The Fortune. Channing played the part of Betty Rizzo in the hit musical Grease and of Peter Falk's unpretentious but determined secretary in Neil Simon's The Cheap Detective, both in 1978. On the basis of these successes, CBS offered her the lead in two short-lived television sitcoms, Stockard Channing in Just Friends (1979) and The Stockard Channing Show (1980).

In the 1980s and 1990s, Channing continued to work in television and film. She also returned to the stage, winning the 1985 Tony Award for a revival of Peter Nichols' A Day in the Death of Joe Egg. In 1990, she played a giant cockroach in Michael Lehmann's Meet the Applegates.

In 1999, Channing took the role of First Lady Abbey Bartlet in the television series The West Wing. She was a recurring guest star for the show's first two seasons, however her increasing importance and noted chemistry with Martin Sheen, who played her husband President Josiah Bartlet saw her become a main cast member of the show in 2001. In the show's seventh and final season (2005-2006), Channing's appearances significantly decreased due to her other role on CBS comedy television series, alongside Henry Winkler and Paula Marshall, in Out of Practice (about a family of doctors). She was, however, seen on The West Wing's last episodes in April and May of 2006. Out of Practice was canceled by CBS after one season.

Channing has won numerous acting awards for various works, including the 1979 People's Choice Award for Favorite Motion Picture Supporting Actress, the 1989 CableACE Award for Best Actress in a Dramatic or Theatrical Special (for Tidy Endings), the 2003 London Critics Circle Film ALFS Award for Actress of the Year (for The Business of Strangers), and the 2003 Screen Actors Guild Award for Outstanding Performance by a Female Actor in a Television Movie or Miniseries (for The Matthew Shepard Story). In 2002, Channing won two Emmy Awards; for Outstanding Supporting Actress in a Drama Series (The West Wing) and Outstanding Supporting Actress in a Miniseries or a Movie (The Matthew Shepard Story). In early July 2006, she received an Emmy nomination for Outstanding Lead Actress in a Comedy Series for her performance in the then-canceled Out of Practice. Channing has also been nominated for a number of other awards, including the 1994 Academy Award for Best Actress (for Six Degrees of Separation).

Channing has been married and divorced four times, to Walter Channing (whose surname she kept), Paul Schmidt, David Debin and David Rawle. Since 1988, she has been in a relationship with cinematographer Daniel Gillham, whom she met on the set of A Time of Destiny. The couple reside in Maine, when she is not working in Los Angeles or New York City. In a 2002 interview, Channing jokingly said of the relationship: "The only one that wasn't a marriage lasts 15 years!"

Stockard Channing made headlines on December 14, 2004, when she was arrested and charged with driving under the influence after being stopped while driving on the shoulder of the Hollywood Freeway in Los Angeles; she spent a few hours in custody and was released without bail. In early October 2005, she pleaded no contest to driving under the influence. Channing was fined $390, given three years' probation, and ordered to attend an alcohol education class.