Stevenson was the great-grandson of a brother of Adlai E. Stevenson, Vice President of the United States (Edgar McLean Stevenson (Sr.) appears on p. 138 of Samuel Harris Stevenson et al., A History and Genealogical Record of the Stevenson Family from 1748 to 1926 (2nd. ed., n.p., n.d.)). He was therefore also a second cousin (once removed) of Adlai Stevenson II who was governor of Illinois and two time Democratic presidential nominee, a first cousin (twice removed) of Lewis G. Stevenson, the Secretary of State of Illinois, and a third cousin of Adlai Stevenson III, an Illinois senator. He is also the brother of actress Ann Whitney.

After serving in the Navy, he attended Northwestern University, where he graduated with a bachelor's degree in theater arts. Afterwards he worked on a radio station, played a clown on a live TV show in Dallas, became an assistant director at Northwestern, and sold medical supplies and insurance. Afterwards he worked as a press secretary for his cousin in the presidential elections of 1952 and 1956. He formed the "Young Democrats for Stevenson".

In 1961, his cousin invited him to some parties, where he met some business luminaries. He followed his cousin's advice to look for a show business career. He auditioned and won a scholarship to the American Musical and Dramatic Academy. His teachers included the well-respected Lee Strasberg, Sandy Meisner, David Craig, Lehman Engel, and Sue Seaton.

Stevenson made his professional career debut in "The Music Man" in 1962 and appeared regularly in Warsaw, Indiana in summer stock productions. After this he appeared in New York on stage and television commercials. He also performed on Broadway. However, he began to establish himself as a comedy writer, writing for the seminal "That Was the Week that Was", in which Alan Alda appeared, and "The Smothers Brothers Comedy Hour". He performed occasionally on both shows.

After guest-starring on "That Girl" (1966) with Marlo Thomas, he was cast in The Doris Day Show in 1969, playing magazine editor boss Michael Nicholson until 1971. Originally, he auditioned for the role of Hawkeye Pierce in M*A*S*H, but was convinced to play Henry Blake instead. This role shot him to stardom. He eventually wrote the episode "The Trial of Henry Blake" (US air date: 11/3/73), and provided the story for another, "The Army-Navy Game" (US air date: 2/25/73). He received one Emmy nomination for his writing.

Henry Blake was one of the most popular characters on M*A*S*H, a carefree clod who preferred fishing to keeping close tabs on the unit under his command. Furthermore, the show quickly became one of the most popular situation comedies running, and would eventually become recognized as one of the top sitcoms in television history. Stevenson, however, began chafing at the fact he was playing second fiddle to the wisecracking Hawkeye (played by Alan Alda), as did Wayne Rogers, and asked to be let out of his contract during the show's third season. The writers reluctantly accomplished this transition in the final episode of the 1974-75 season, in which Col. Blake was discharged, only to board a plane that was shot down over the Sea of Japan, killing everyone on board.

Stevenson's departure from M*A*S*H turned out to be one of the most catastrophic show-business career decisions in entertainment history. Stevenson starred in a series of sitcoms that he hoped would bring him the comic leading-man status to which he aspired. None of these efforts met with much success. They included The McLean Stevenson Show, In the Beginning, Hello, Larry, and Condo. All four sitcoms were dismissed by audiences and critics alike as sorry wastes of Stevenson's abilities. Not one show lasted more than a single season (though Hello, Larry lasted a season and a half).

Stevenson also guest-starred in shows such as Square One TV, The Love Boat, Diff'rent Strokes, Match Game, Hollywood Squares, and The Tonight Show Starring Johnny Carson. His screen credits include the Disney movie The Cat from Outer Space as a friend of Dr. Frank Wilson (played by Ken Berry). In 1981, Match Game host Gene Rayburn described Stevenson as someone "responsible for the demise of several television shows", in jest. However, this statement is true even though it was used as a joke. This is a stereotype of McLean that most Americans share. Coincidentally, Match Game was cancelled in 1982, a little less than a year after Stevenson was pitched as a regular panelist.

Stevenson was recovering from surgery in a Los Angeles hospital on February 15, 1996 when he unexpectedly went into cardiac arrest and died. It was two months after his 66th birthday. In a strange twist of fate, Stevenson was the first cast member from M*A*S*H to leave the series, as well as the first to die. M*A*S*H writer Larry Gelbart later said that Stevenson had left too soon twice in one lifetime.

Stevenson is interred in Forest Lawn - Hollywood Hills Cemetery in Los Angeles. He left behind a wife Ginny, daughter Lindsey and actor Jeff MacGregor (from a previous marriage). Coincidentally, Roger Bowen, who had played Henry Blake in the M*A*S*H movie, also died of cardiac arrest the day after Stevenson's passing.

Shortly before his passing, Stevenson admitted that he regretted leaving M*A*S*H when he did. One legacy of Stevenson is a word coined from his first name, McLean--McLeaning, which refers to an actor leaving a show, and his or her character's subsequent demise--as happened to Henry Blake when McLean Stevenson left M*A*S*H.