Physicist Dr. Reed Richards is convinced evolution was triggered millions of years ago on Earth by clouds of cosmic energy in space, and has calculated that one of these clouds is soon going to pass near Earth. Together with his friend, astronaut Ben Grimm, Richards convinces Dr. Victor von Doom, his former classmate at MIT and now CEO of Von Doom Industries, to allow him access to his privately owned space station to test the effects of a biological sample of exposure to the cloud. Doom agrees in exchange for control over the experiment and a majority of the profits from whatever benefits it brings. Richards brings aboard his ex-girlfriend and Von Doom's chief genetics researcher Susan Storm and her hot-headed ex-astronaut brother Johnny.
The quintet travels to outer space to observe the cosmic energy clouds, but Richards miscalculates and the clouds materialize ahead of schedule. Richards and the Storms leave the shielded station to rescue Grimm, who had gone on a spacewalk to place the samples. Grimm receives full exposure in outer space, while the others receive a more limited dose within the station. Back home they soon develop superpowers: Richards can stretch his body like rubber, Susan Storm can become invisible and generate impact resistant force shields, Johnny Storm can engulf himself in fire and fly unaided, and Grimm becomes a rocklike creature with superhuman strength and durability. Meanwhile, von Doom faces a backlash from his stockholders because of the publicity from the space mission, and has a scar on his face that came from an exploding control console on the station.
Grimm's fiancee Debbie cannot handle his new appearance and decides to leave him. Grimm goes to brood on the Brooklyn Bridge and accidentally causes a traffic pileup while preventing a man from jumping off the bridge. Grimm, Richards and the Storms use their various abilities to contain the damage and prevent harm. The media dubs them the Fantastic Four. They move into Richards' lab in the Baxter Building to study their abilities and seek a way to return Grimm to normal. Von Doom, himself mutating, offers his support but blames Richards for the failure of the spaceflight, which has lost him his company.
Richards tells the group he will construct a machine to recreate the storm and reverse its effects on them, but warns it could possibly accelerate them instead. Meanwhile von Doom's arm has become organic metal, allowing him to produce bolts of electricity, and he begins plotting revenge. He drives a wedge between Grimm and Richards, who has rekindled his relationship with Susan Storm. Using the machine, von Doom restores Ben to human form, while accelerating von Doom's condition, causing much of his body to turn to metal. Von Doom knocks the human Grimm unconscious and captures Richards.
Now calling himself Doctor Doom, he puts on a metallic mask to hide his disfigurement, tortures Richards and fires a heatseeking missile at the Baxter Building in an unsuccessful attempt to defeat Johnny Storm. Susan Storm confronts Doom but is outmatched. Grimm arrives to assist her, transformed into the Thing again by reusing the machine (speaking his signature line, "It's clobberin' time!"). The battle then gets spilled into the streets and The Storms combine their powers to wrap Doom in an inferno of intense heat, and Grimm and Richards douse him with cold water, inducing thermal shock and freezing Doom in place. In an epilogue, Grimm informs Richards that he has accepted his condition with the help of Alicia Masters, a blind artist for whom he has developed feelings, and the team embraces its role as superheroes. Richards proposes marriage to Susan Storm, who accepts. Meanwhile, Doom's statue-like remains are being transported back to his homeland of Latveria when the dockmaster's electronic manifest briefly undergoes electromagnetic interference, suggesting that Doom is alive.