Reds boss Sir Alex Ferguson said: "Chris is an extremely talented young defender, who we have been monitoring for some months. He’s very quick and reads the game well. He will be a great asset to the club, playing alongside some of the best defenders around and we’re delighted to have secured his signature."
Smalling, 20, described the move as an "unbelievable opportunity".
"My time at Fulham has been great and I have learned a lot about the game from Roy Hodgson and the coaching staff," he said. “But the chance of coming to the biggest club in the world is something I just couldn’t turn down. I’m excited about working with Sir Alex and the fantastic players in the squad.
"I’ve played a few times in the Europa League this year, but the thought of making the step up to the Champions League next year is great. I can’t wait.”