Kline was born in St. Louis, Missouri, to Margaret Agnes Kirk and Robert Joseph Kline (1909-1996). His father was a classical music lover and an amateur opera singer who owned and operated The Record Bar, a record store in St. Louis that opened in the early 1940s, and sold toys during the 1960s and 1970s; his father's family also owned Kline's Inc., a department store chain. Kline has described his mother as the "dramatic theatrical character in our family". Kline's father was Jewish, from a family that had emigrated from Germany, and had become an agnostic. Kline's mother was a Roman Catholic of Irish descent, the daughter of an emigrant from County Louth. Kline was raised in his mother's Catholic faith. He has three siblings, Alex, Christopher, and Kate.

He graduated from the Saint Louis Priory School in 1965. In 1997, the school named its new auditorium as the Kevin Kline Theater in his honor. Kline performed selections from Shakespeare as a benefit at the dedication.

In 1970, Kline was awarded a scholarship to the newly formed Drama Division at the Juilliard School in New York. In 1972, he joined with fellow Juilliard graduates, including Patti LuPone and David Ogden Stiers, and formed the City Center Acting Company (now The Acting Company), under the aegis of John Houseman.

Kline began his career on stage in 1972 with The Acting Company. He has gone on to win three Tony Awards for his work on Broadway, winning Best Featured Actor in a Musical for the 1978 original production of On the Twentieth Century, Best Actor in a Musical for the 1981 revival of The Pirates of Penzance, and Tony Award for Best Actor in a Play for the 2017 revival of Present Laughter.

In 1976, Kline left The Acting Company and settled in New York City, doing a brief appearance as the character "Woody Reed" in the now-defunct soap opera Search for Tomorrow. He followed this with a return to the stage in 1977 to play Clym Yeobright opposite Donna Theodore as Eustacia Vye in The Hudson Guild Theater production of Dance on a Country Grave, Kelly Hamilton's musical version of Thomas Hardy's The Return of the Native. In 1978, he played the role of Bruce Granit, a matinée idol caricature, in Harold Prince's On the Twentieth Century, for which he won his first Tony Award. In 1981, Kline appeared with rock diva Linda Ronstadt and singer Rex Smith in the New York Shakespeare Festival's Central Park production of The Pirates of Penzance, winning another Tony Award for Best Leading Actor in a Musical, for his comically dashing portrayal of the Pirate King. In 1983, he played the role in a film version of the musical, also with Ronstadt, Smith and Angela Lansbury, which had a limited theatrical release.

During the 1980s and early 1990s, Kline made several films with Director Lawrence Kasdan, including The Big Chill, Silverado, Grand Canyon, I Love You to Death, and French Kiss. He played Donald Woods in Richard Attenborough's Cry Freedom opposite Denzel Washington about the friendship between Activist Stephen Biko and Editor Donald Woods.

Dubbed "the American Olivier" by New York Times theater critic Frank Rich for his stage acting, Kline finally ventured into film in 1982 in Sophie's Choice. He won the coveted role of the tormented and mercurial Nathan opposite Meryl Streep. Streep won an Academy Award for her performance in the film. Kline was nominated for a 1983 Golden Globe award (New Star of the Year) and BAFTA Award for Most Outstanding Newcomer To Film.

Kline met Actress Phoebe Cates in 1983 and they were married in 1989. The couple lived in New York City and they have two children, Owen (born 1991) and Greta.

Other awards have included Drama Desk Awards, Golden Globe awards, a Gotham Award, a Hasty Pudding Theatricals Man of the Year Award, and a St. Louis International Film Festival Lifetime Achievement Award. He was inducted in the American Theatre Hall of Fame in 2003. He has a star on the St. Louis Walk of Fame. Film reviewers have praised Kline. Newsday critic Lynn Darling wrote on July 13, 1988, that Kline "has proved himself to be one of the most talented and versatile American actors of his generation."

In 1989, Kline won an Academy Award for Best Supporting Actor for his role in the British comedy A Fish Called Wanda, in which he played a painfully inept American ex-CIA thug opposite John Cleese's genteel British barrister and Jamie Lee Curtis' femme fatale/con woman. In 2000, the American Film Institute ranked the film twenty-first on AFI's 100 Years... 100 Laughs.

He also appeared in a Lincoln Center production that combined the two parts of Henry IV on Broadway at the Vivian Beaumont Theatre in 2003 as Falstaff. Kline was nominated for the 2004 Tony Award, Actor in a Play.

After his son, Owen, was diagnosed with Juvenile diabetes, Kline became active with the Juvenile Diabetes Research Foundation. In November 2004, he was presented with the JDRF's Humanitarian of the Year award by Meryl Streep for his volunteer efforts on behalf of the organization.

In January 2008, Kline won a Screen Actors Guild award for his portrayal of Jaques in Kenneth Branagh's film As You Like It, adapted from Shakespeare's play. The film premiered theatrically in 2006 in Europe. It bypassed theatres and was sent straight to HBO in the U.S. Kline's film The Conspirator premiered during the Toronto International Film Festival in 2010 and was described as an "old-fashioned historical thriller". It was well received by most critics. Kline also starred in the 2012 comedy Darling Companion alongside Diane Keaton. In 2017, Kline returned to Broadway in a revival of the play Present Laughter, for which he received his third Tony Award.