Nelson died at his Century City home of complications from colon cancer, said publicist Dale Olson.
In 1949, the popular show became a true family affair when 12-year-old David and 8-year-old Ricky replaced the child actors who had been portraying them on radio.
"The Adventures of Ozzie and Harriet" moved to television three years later, debuting on ABC in October 1952.
When the series ended in 1966 after 435 episodes, it had become the longest-running family situation comedy in TV history — as well as serving as the launch pad and showcase for teen idol Rick Nelson's singing career.
In the process of playing fictionalized versions of themselves on television each week for 14 years, David and Rick Nelson literally grew up in front of millions of Americans.
Indeed, after David and Rick were married in the early '60s, their wives — first David's wife, actress June Blair, and then Rick's wife, the former Kris Harmon — became their TV wives.
The blurring of what was real and what was not real caused confusion in some viewers' minds.
When David enrolled at USC and joined a fraternity after graduating from Hollywood High School in 1954, his TV character started college and joined a fraternity.
But unlike his TV character, who became a lawyer on the show, David did not go into law.
Instead, he launched his career as a director by taking the reins from his director-father for about a dozen episodes of the show in the early '60s. He spent the next several decades directing commercials and occasional TV series and movies.
"The Adventures of Ozzie and Harriet" has been criticized for presenting an idealized version of American family life that few could live up to.
That included the Nelsons, as David pointed out in a 1971 Esquire article headlined "The Happy, Happy, Happy Nelsons."
"We would keep up the front of this totally problemless, happy-go-lucky group," he said. "There might have been a tremendous battle in our home, but if someone from outside came in, it would be as if the director yelled, 'Roll 'em,' We'd fall right into our stage roles.
"It's an awfully big load to carry, to be everyone's fantasy family."
He was born Oct. 24, 1936, in New York City, when Ozzie and Harriet were in their big-band heyday.
Rick was born in 1940, the year before the Nelsons moved permanently to Hollywood.
After Ozzie and Harriet launched their radio show in 1944, David and Rick would accompany their parents to their live broadcasts.