"Chris is an extremely talented young defender, who we have been monitoring for some months," United manager Alex Ferguson told the club website.
"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."
The England under-21 defender moved for an undisclosed fee but will stay with Fulham for the rest of the season before joining United in July.
The 20-year-old has enjoyed a rapid rise since joining from non-league Maidstone United 18 months ago. He has made only 10 first-team appearances for Roy Hodgson's Fulham.
"My time at Fulham has been great and I have learned a lot about the game from Roy Hodgson and the coaching staff," Smalling 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."
Smalling, who had also interested Arsenal, will be in 10th-placed Fulham's squad for Saturday's match at home to Aston Villa.
"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," he added.
