In 2032, he was the commander of the Ares IV mission to Mars. He disappeared on October 19, along with the command module in which he was orbiting the planet, while the other two crewmembers were on the planet's surface.
Unfortunately for him, a graviton ellipse appeared out of nowhere and engulfed his ship, which left him trapped without communication to the rest of the universe. There, he found an alien spaceship, or more specifically, the broken fragments of one. He managed to survive for ten days, but then rerouted all power on his craft to the imager, leaving him to die of hypothermia.
USS Voyager subsequently discovered the command module, along with Kelly's body, inside the graviton ellipse in the Delta Quadrant in 2376. Accessing the logs, they learned, much to their surprise, that Kelly had lived for several days after being caught in the ellipse, learning that Humans were not alone in the universe before he died. Kelly was given a full military funeral aboard Voyager, and was widely regarded as one of the true pioneers of manned space exploration, a fact which was even acknowledged by Seven of Nine, who had initially been skeptical of the value in his recovery.
Kelly was a fan of the New York Yankees baseball team, and regretted he would never know who won the World Series in 2032. At his funeral service on the bridge of Voyager, Seven walked over to his coffin and whispered, "the Yankees... in six games." (VOY: "One Small Step")