In the pilot episode, "The Lady in the Bottle", astronaut Captain Tony Nelson, United States Air Force, is on a space flight when his one-man capsule Stardust One comes down far from the planned recovery area, near a deserted island in the South Pacific. On the beach, Tony notices a strange bottle that rolls by itself. When he rubs it after removing the stopper, smoke starts shooting out and a Persian-speaking female genie materializes and kisses Tony on the lips, shocking him.

They cannot understand each other until Tony expresses his wish that Jeannie (a homophone of genie) could speak English, which she then does. Then, per his instructions, she "blinks" and causes a recovery helicopter to show up to rescue Tony, who is so grateful, he tells her she is free, but Jeannie, who has fallen in love with Tony at first sight after being trapped for 2,000 years, re-enters her bottle and rolls it into Tony's duffel bag so she can accompany him back home. One of the first things Jeannie does, in a subsequent episode, is break up Tony's engagement to his commanding general's daughter, Melissa, who, along with that particular general, is never seen or mentioned again. Producer Sidney Sheldon realized the romantic triangle between Jeannie, Tony, and Melissa would not pan out in the long run.

Tony at first keeps Jeannie in her bottle most of the time, but he finally relents and allows her to enjoy a life of her own. However, her life is devoted mostly to his, and most of their existential problems stem from her love for him and her often-misguided efforts to please him, even when he does not want her assistance. His efforts to cover up Jeannie's antics, because of his fear that he would be dismissed from the space program if her existence were known, brings him to the attention of NASA's resident psychiatrist, U.S. Air Force Colonel Dr. Alfred Bellows. In a running gag, Dr. Bellows tries over and over to prove to his superiors that Tony is either crazy or hiding something, but he is always foiled ("He's done it to me again!") and Tony's job remains secure. A frequently used plot device is that Jeannie loses her powers when she is confined in a closed space. She is unable to leave her bottle when it is corked, and under certain circumstances, the next person who removes the cork becomes her new master. A multiple-episode story arc involves Jeannie (in miniature) becoming trapped in a safe when it is accidentally locked.