Born to Robert Joseph Kline (a German-born Jew) and Agnes Delaney (an Irish American Catholic), second of four children, Kline was raised in his mother's faith and graduated from the Roman Catholic Saint Louis Priory School in 1965, afterwards attending Indiana University in Bloomington, Indiana, where he began as an aspiring classical pianist. He joined the on-campus theater group the "Vest Pocket Players" and fell in love with the theater as an undergraduate.

In 1970 he was awarded a scholarship to the newly-formed Juilliard Drama 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 famed British actor John Houseman. The Company traveled across the U.S. performing Shakespeare and other classical works, founding a dedication and mission unparalleled in American repertory theatre.

In 1976, Kline left The Acting Company and settled in New York City, doing a brief stint as the character "Woody Reed" in the now defunct soap opera Search for Tomorrow. This was followed in 1978 by a small role as "Bruce Granit", a matinee' idol caricature, in Hal Prince's On The Twentieth Century for which Kline won his first Tony Award.

In 1981, Kline paired up with rock diva Linda Ronstadt and singer Rex Smith in the New York Shakespeare Festival's Central Park production of The Pirates of Penzance, garnering another Tony Award for Best Leading Actor in a Musical, for his comically dashing portrayal of the Pirate King. He later played the role in a film version of the musical, also with Ronstadt, which had a limited theatrical release.

In ensuing years, Kline appeared many times in New York Shakespeare Festival productions of Shakespeare, including title roles in Richard III, Much Ado About Nothing, Henry V, and two productions of Hamlet, one of which he also directed. Dubbed "the American Olivier" by New York Times theater critic Frank Rich for his stage acting, Kline finally ventured into film in 1982, winning the coveted role of the tormented and mercurial "Nathan" opposite Meryl Streep in Alan Pakula's Sophie's Choice (Streep won an Academy Award for her performance in the film)

During the 80s and early 90s, Kline made several films with director Lawrence Kasdan, including The Big Chill, Silverado, Grand Canyon, I Love You To Death, and French Kiss. 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 caricature of a painfully stupid American ex-CIA thug opposite John Cleese's genteel British barrister. In 2000, the American Film Institute ranked the film 21st on AFI's 100 Years... 100 Laughs.

Though he has been offered many roles that could have boosted him to box-office superstardom, Kline has kept a wary distance from the Hollywood star-making machine and developed a reputation for picking parts with discrimination (such as strong roles in Grand Canyon and Life as a House), leading to the industry moniker "Kevin Decline".

Other awards have included New York Drama Desk awards, Golden Globe awards, a Gotham Actor Award, a Hasty Pudding Theatricals Man of the Year Award, and a St. Louis International Film Festival Lifetime Achievement Award. He also has his own star on the St. Louis Walk of Fame.