"Chris has agreed personal terms with the club and will join for the beginning of the 2010-2011 campaign. He will remain at Fulham until the end of the current season," said a statement on the United website.
Smalling played for Fulham in their 2-0 defeat at Tottenham Hotspur later on Tuesday after which the west London club's manager Roy Hodgson confirmed the 20-year-old had agreed to join United from next season.
"The club has accepted an offer from Manchester United and as far as I'm aware that's where he is going," Hodgson told Sky Sports. "As far as I know terms have been agreed.
"He is going for a medical tomorrow and he will be a Manchester United player from next season.
"He is a great talent and we're very proud that we have produced a player of that quality and we would have loved him to play in a Fulham shirt but when Manchester United come calling it's not easy to stand in the boy's way.
"I can only congratulate (United manager) Alex (Ferguson) on his judgement and I'm sure he will go on to do great things for Manchester United."
England under-21 player Smalling made his first Premier League start against Chelsea in December.
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