Lewis (Jordan Fry), is an aspiring young inventor who was left at an orphanage by his mother when he was an infant. He has yet to be adopted and fears that he never will be. Convinced that his birth mother will want him, he attempts to invent a memory-scanning machine in the hopes that he can find her. He spends all of his time on the project, causing his roommate Mike Yagoobian (Goob) to stay awake for days. This makes Goob fall asleep during an important little league game.

At Lewis' school science fair, Lewis is approached by a mysterious boy named Wilbur Robinson (Wesley Singerman), who claims to be a "time cop" from the future. Wilbur says that a man wearing a bowler hat has stolen a time machine that Wilbur wishes to recapture. The sinister 'Bowler Hat Guy' (Stephen J. Anderson), sends Doris (Ethan Sandler), a robotic bowler hat with mechanical arms, to sabotage Lewis' memory-scanner. As Lewis begins demonstrating the use of his machine, it explodes, throwing the science fair into chaos. Lewis runs out, and the Bowler Hat Guy steals his unattended memory scanner. Wilbur tells Lewis to go back to the science fair and fix the machine. To prove to a suspicious Lewis that he is from the future, Wilbur takes him to a flying time machine to take them to year 2037, thirty years in the future.

While giving Lewis a tour of the fantastical world of the future, Lewis realizes he can use the time machine to go back and actually see his mother, since he knows the date he was left at the orphanage. Wilbur insists he go back to fix the memory scanner instead, and while arguing, they crash the time machine. Wilbur asks Lewis to fix it, and Lewis agrees under the condition that Wilbur take him back to visit his mother afterwards. Wilbur tries to hide Lewis in the garage of his house, but Lewis leaves and meets Wilbur's grandfather, Bud (Stephen J. Anderson). Bud takes Lewis on a tour of the house, during which Lewis meets the rest of the fun-loving and overly-eccentric Robinson family, which consists of adopted people living in a large, stately manor. Wilbur explains that his father, Cornelius, the only member of the Robinson family that Lewis did not meet, invented several of the futuristic inventions earlier seen, coining the motto "Keep moving forward".

Meanwhile, Bowler Hat Guy and Doris follow Wilbur and Lewis to the future and attempt to kidnap Lewis so he can show them how his memory scanner works. Meanwhile, the Robinsons offer to adopt Lewis but change their mind when they discover that he's from the past. Lewis runs away in misery after finding out Wilbur lied to him about going back to see his mom, and encounters the Bowler Hat Guy, who lures him into his time machine by promising to bring him to his mother.

Instead, the Guy brings him to Lewis' orphanage, at some point after 2007, when it has been shut down and abandoned. The Guy reveals himself as an aged and deeply embittered Mike Yagoobian. He also reveals that "Cornelius Robinson" is Lewis, making Wilbur his son and the Robinsons his family. Goob explains that he blames Lewis for his miserable life, which began a downward spiral with the little league game he fell asleep in. He later met DOR-15 (Doris), a failed and abandoned invention of Lewis'. They co-operate to steal the time machine and plotted to use it to capture and plagiarize Lewis' first famous invention, to ruin Lewis' career as an inventor.

Goob and Doris prepare to present the stolen invention to a corporation in the present. Meanwhile, Wilbur and his robot Carl (Harland Williams) save Lewis and escape, but Doris destroys Carl. As Goob makes the sale to the corporation, the scenery around Lewis and Wilbur in the future darkens, and Wilbur vanishes into oblivion as history is rewritten. Lewis enters the derelict house where the Robinsons once lived, and discovers the memory-scanner in the garage. Viewing its records, he discovers that after mass-producing the memory-scanner, Goob also mass-produces Doris, whereupon the multitude of robotic hats took control of their wearers, something Goob hadn't planned. The utopian future is replaced by a Doris-controlled, smog-darkened industrial empire, with mankind reduced to mindless slaves.

Pursued by an army of DOR-15 hats, Lewis manages to repair the time machine and uses it to go to the precise moment and location where Goob signed the contract at InventCo. Lewis causes Doris to disappear into oblivion by promising that he will never invent her. Lewis then shows Goob the bleak future Doris would have created, which is transformed before their eyes back into the utopian future. After they land near the Robinson house, Wilbur is brought back into existence. Lewis gets Wilbur to offer for the Robinsons to adopt Goob, but Goob, ashamed of what he has done, hides and then walks off, uncertain of what to do.

"Cornelius" (Tom Selleck) finally returns from his business trip and meets his younger self, giving him a helpful speech. Wilbur fulfils his promise to Lewis by visiting the moment at which his mother abandoned him. Lewis nearly interrupts her from leaving the infant at the orphanage, but inexplicably decides not to, abandoning his lifelong dream.

Finally, Lewis returns to the present and prevents Goob from becoming the Bowler Hat Guy by waking him up in time to catch the ball that wins him the game. Lewis then returns to the science fair and demonstrates his memory scanner on the science fair judge, Dr. Krunkelhorn (Laurie Metcalf), revealing that she is Wilbur's grandmother, Lucille. Lewis also meets a young Franny. Bud and Lucille adopt Lewis, nicknaming him "Cornelius", as it seems to suit him, and Lewis quickly sets to work building Carl in an observatory bought by Bud and Lucile which will one day become the Robinson house. Just before Lewis drives off with Bud and Lucille, he turns around and waves at Goob, who is also leaving the orphanage with his own new family. Bud and Lucille move into the house Lewis saw further in time where he continues his inventing, fulfilling his future.

As the fusion between Disney and Pixar occurred during the production of the film, John Lasseter became the chief creative officer for the Walt Disney Company. When he saw an early screening for the movie, he told the director Stephen Anderson that he didn't find the villain scary or threatening enough, and suggested that he make some changes.