The film opens with a trio of arrogant young blue birds harassing their youngest sibling Buster (Blaze Berdahl). As Buster leaves his family, he meets an intelligent golf-playing Orange Tyrannosaurus Rex named Rex (John Goodman). Rex explains to Buster that he was once a stupid and violent dinosaur, and proceeds to tell the story of how he came to become what he is today.
Millions of years in the past, Rex is a savage creature who terrorizes smaller animals until a futuristic aircraft arrives and interrupts Rex's rampage. Rex is greeted by a small green creature named Vorb (Jay Leno) who feeds him "Brain Grain", a cereal that increases Rex's intelligence. The inventor of the cereal and pilot of the aircraft, Captain Neweyes (Walter Cronkite), brings in Rex, gives him his name, and introduces him to Pooh And His Friends And other dinosaurs that have been fed Brain Grain: Dweeb the Green Parasaurolophus (Charles Fleischer), Woog the Blue Triceratops (Rene LeVant) and Elsa the Lavender Pteranodon (Felicity Kendal). Neweyes then reveals his goal of allowing the children of the present time to see real dinosaurs, fulfilling their biggest wishes. He informs them that there are two people to keep an eye out for: Doctor Juliet Bleeb (Julia Child), a scientist from the Museum of Natural History who will aid the dinosaurs, and Professor Screweyes (Kenneth Mars), Neweyes's insane twin brother. He instructs them to find Doctor Bleeb and avoid Professor Screweyes.
Neweyes drops the dinosaurs off at the Hudson River where they meet a young raft-sailing boy named Louie (Joey Shea), who plans on literally running away to join the circus. Upon reaching New York City, Louie realizes that people would panic if they saw live dinosaurs and, with the help of Elsa, flies over the city in search of a good hiding place. During the flight, Louie comes across a girl named Cecilia Nuthatch (Yeardley Smith). Cecilia explains that her parents are hardly around. Louie convinces Cecilia to abandon her home and introduces her to the dinosaurs (Louie and Cecilia then quickly develop a crush on each other). When the dinosaurs explain their goal of getting to the Museum of Natural History, Louie decides to disguise them as floats in the Macy's Thanksgiving Day Parade. During the parade, Rex hears all the children wishing to see real dinosaurs, so he starts to sing the song "Roll Back the Rock (To the Dawn of Time)." When the audience realizes that live dinosaurs are among them, they fly into a panic. The local authorities are called in to stop the dinosaurs, resulting in a slapstick-filled chase scene. As the dinosaurs lose the cops, Louie and Cecilia venture to Central Park, where Professor Screweyes is running his "Eccentric Circus". Louie and Cecilia meet Professor Screweyes and cite their desire to join his circus. As they literally sign a contract in blood, the dinosaurs arrive and try to save them. Screweyes, upon meeting the dinosaurs, explains that he delights in scaring people and believes that the dinosaurs would make a great addition to his circus. He then reveals his very own "Brain Drain", the polar opposite of his brother's Brain Grain. He demonstrates the Brain Drain on Louie and Cecilia, devolving them into chimpanzees as he makes the dinosaurs a deal: if the dinosaurs consume the Brain Drain and join his circus, he'd destroy the contract and let Louie and Cecilia free. Reluctantly, the dinosaurs accept the offer.
As Louie and Cecilia return to their human forms and awake the next morning, they are greeted by a circus clown named Stubbs (Martin Short). Upon seeing the dinosaurs returned to their natural vicious states, Louie and Cecilia plan to sneak into that night's show and save the dinosaurs. During the performance, the dinosaurs break loose and try to attack Screweyes. However, Louie steps in and desperately tells the devolved Rex that it wouldn't be right to eat Screweyes. These impassioned pleas serve to return the dinosaurs to their friendly natures. Just then, Captain Neweyes arrives in his aircraft and congratulates Louie and Cecilia who proceed to kiss in front of a whole crowd of people. After Stubbs arrives to resign from Professor Screweyes's employ, Captain Neweyes, Louie, Cecilia and the dinosaurs board the aircraft, leaving Screweyes to be devoured by the crows that have been present whenever he has in the movie. The dinosaurs spend the rest of their days in the Museum of Natural History, allowing children to see live dinosaurs. Meanwhile, Louie and Ceilia reconcile with their respective parents, and the two become a couple, Rex returns Buster to his family.