Stevenson was born in the town of Normal, Illinois, in McLean County. A member of the Stevenson family He was the great-grandson of William Stevenson, second cousin, once removed, of Presidential Candidate Adlai Stevenson II. He was also the brother of actress Ann Whitney. His father, Edgar, was a cardiologist.

Stevenson was educated at Lake Forest Academy and thereafter joined the Navy. After his service, he attended Northwestern University, where he graduated with a bachelor's degree in theater arts and was a proud and well-liked Phi Gamma Delta (Fiji) fraternity brother. Afterwards he worked at 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. He also 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.

During this period, he also appeared in TV commercials for products like Winston cigarettes, in which he was shown sprinting around a parking lot of Winston delivery trucks and painting over the product slogan, replacing the "like" in "like a cigarette should" with the grammatically correct "as."

After guest-starring on That Girl 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," and provided the story for another, "The Army-Navy Game." He received an Emmy nomination for his writing.

Stevenson found his greatest success on the amazing series M*A*S*H. The series quickly became one of the most popular situation comedies running, and was eventually recognized as one of the top sitcoms in television history. Despite the show's success, Stevenson began chafing (as did Wayne Rogers) at playing second fiddle to the wisecracking Hawkeye (played by Alan Alda), and asked to be released from his contract during the show's third season. The show's writers reluctantly penned him an exit in the final episode of the 1974-75 season, in which Lt. Colonel Blake was discharged, only to board a plane that was shot down over the Sea of Japan, killing everyone on board (a development added after scripts were distributed so the show's actors would display genuine emotion as if they had been truly unaware of that part of the storyline). Stevenson later admitted that leaving M*A*S*H was a mistake, and he was also upset by the fact that his character's death prevented him from returning to the show.

In an interview, Loretta Swit shed some light on the subject of why McLean left the series at the height of its success. She said Stevenson wanted to be number one and felt pushed down as one of an ensemble of eight. Swit said that before Stevenson left the series he told her, "I know I will not be in anything as good as this show, but I have to leave and be number one."

Stevenson appeared as a guest panelist for several weeks on Match Game in 1973, and again in 1978 on the daytime and nighttime syndicated version. In 1981, Stevenson became a regular panelist on the Match Game's syndicated version. Host Gene Rayburn described Stevenson as someone "responsible for the demise of several television shows" just before handing Stevenson Match Game hosting duties for a day. Stevenson remained a panelist until the show was cancelled in 1982.

After his departure from M*A*S*H, Stevenson's acting career began to decline. He starred in a series of sitcoms, none of which lasted more than approximately one season. They included The McLean Stevenson Show (1976), In the Beginning (1978), Hello, Larry (1979–80) and Condo (1983). All four sitcoms were dismissed by audiences and lambasted by critics.