In 1965, following the success of his TV series Gilligan's Island, Sherwood Schwartz conceived the idea for The Brady Bunch after reading an article in the Los Angeles Times that said "40% of marriages [in the United States] had a child or children from [a] previous marriage." He instantly set to work on a pilot script, called Yours and Mine, and passed it around the "big three" television networks of the era. ABC, CBS and NBC all loved the script, but each network wanted changes to it before they would commit to filming it. Schwartz felt that his script was perfect, and although he had the interest of all three networks in America, he decided to shelve it.

Despite the similarities between the series and the 1968 theatrical release Yours, Mine and Ours starring Henry Fonda and Lucille Ball, the original script for The Brady Bunch predated the script for the film. However, the success of the film was a factor in ABC's decision to order episodes for the series.

Mike Brady (Robert Reed), widowed architect with sons Greg (Barry Williams), Peter (Christopher Knight) and Bobby (Mike Lookinland), marries Carol Martin (née Tyler) (Florence Henderson), whose daughters are Marcia (Maureen McCormick), Jan (Eve Plumb) and Cindy (Susan Olsen). The wife and daughters take the Brady surname. Producer Schwartz wanted Carol to have been a divorcée but the network objected to this. A compromise was reached whereby no mention was made of the circumstances in which Carol's first marriage ended, but many assume she was widowed. The newly formed juvenile sextet, parents Carol and Mike, Mike's live-in housekeeper Alice (Ann B. Davis), and the boys' dog Tiger settle into a large, suburban home designed by Mike. Though the writers carefully avoid any mention of the Bradys' specific location during the series, the show clearly takes place in Southern California, presumably Los Angeles.

The theme song penned by Schwartz quickly communicated to audiences that the Bradys were a blended family. In the first season this blending figured prominently in episode stories; from the second season it was less intrinsic to stories but would be casually referred to in dialogue. Two episodes from the third season, "Not So Rose Colored Glasses" and "Jan's Aunt Jenny," mention that Mike and Carol had been married for three years. In the "Kelly's Kids" episode of the final season, further reference was made to the Bradys' adoptions ("Either way, you adopted three boys and you adopted three girls, right?") when their neighbors, the Kellys, adopted three boys of different races.

It was not the first series to show a "blended" family (two series which debuted in the 1950s, Make Room For Daddy and Bonanza, had stepsiblings and half-siblings respectively), but came at a time when divorce and remarriage in America was seeing a surge. Episodes in the first season chronicled the family learning to adjust to its new circumstances and become a unit, as well as typical childhood problems such as rivalries and family squabbles, and the fact that their house had four bedrooms for two married adults, one housekeeper, and six children. Over time the episodes focused more on issues related to the kids growing up, such as dating, self-image, responsibility, and even puberty.

Subtle references to larger social problems found their way into the dialogue from time to time. For example, in one social-issue episode, season two's "The Liberation of Marcia Brady", Marcia sets out to prove a girl can do anything a boy can. The boys find this very upsetting and Peter finds himself joining the Sunflower Girls, Marcia's club, in hopes of making her back down.

In 1971, due to the success of the Bradys' ABC Friday night companion show The Partridge Family (about a musical family), some episodes began to feature the Brady Kids as a singing group. Though only a handful of shows actually featured them singing and performing ("Dough-Re-Mi" in the third season, "Amateur Nite" in the fourth and "Adios, Johnny Bravo" in the fifth), the Brady Bunch began to release albums. Though they never charted as high as the Partridges, the cast began touring the United States during the summer hiatus from the show, headlining as The Kids from the Brady Bunch. Only Barry Williams and Maureen McCormick stayed in the music business as adults. Christopher Knight readily admits he felt he could not sing and recalls having great anxiety about performing live on stage with the cast.

The Brady Bunch never achieved high ratings during its primetime run (never placing in the top 25 during the five years it aired) and was canceled in 1974 after five seasons and 117 episodes. At that point in the story Greg graduated from high school and was about to enroll in college. Despite its less-than-stellar primetime ratings and having won no awards, the show would become a true cultural phenomenon, enduring in the minds of Americans and in syndication for decades. The series has spawned several sequel series on the "Big 3" U.S. networks, made-for-TV movies, and parody theatrical releases, as well as a touring stage show and countless specials and documentaries on both network and cable TV.

Since its first airing in syndication in September 1975, an episode of the show has been broadcast somewhere in the United States and abroad every single day of every single year through at least 2008. Reruns were also shown on ABC daytime from July 9, 1973 to August 29, 1975, at 11:30 a.m. Eastern/10:30 Central. The run was interrupted only once, between April 21 and June 27, 1975, when ABC ran a short-lived game show, Blankety Blanks, in that time slot.

When the episodes were repeated in syndication, they usually appeared every weekday in late-afternoon or early-evening slots on local stations. This enabled children to watch the episodes when they came home from school, making the program widely popular and giving it iconic status among those who were too young to have seen the series during its prime time run. The show's longevity in the public mind largely owes to that phenomenon, which was a unique aberration from the traditional norm of a previously-run network program being sold to stations as schedule filler between network programming blocks[citation needed].