The England left-back, who featured for the Three Lions at the World Cup, completed his medical at the club's training ground on Friday, having agreed terms on a lucrative four-year contract, with an option for a fifth.
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Upon completing his move, he told the club's website: "I am thrilled and excited to be joining Manchester United. I have been at Southampton since I was eight years old and I would like to thank them and the fans for everything they have done for me.
"I want to continue to progress my career and joining United is the ideal place for me to do that. I am looking forward to this new chapter in my life and also looking forward to learning from the world-class players and management at the club."
Assistant manager Ryan Giggs added his delight at the signing, saying: "Luke is a very talented young left-back with great potential. He has developed immensely during his time at Southampton and has all the attributes to become a top player.
"I am delighted he has joined Manchester United as I believe this is the right club for him to continue his development as a young player and eventually fulfil that promise."
The 19-year-old becomes the second signing of Louis van Gaal's United reign, with Ander Herrera having completed his move to the club on Thursday.
And Southampton's executive director has revealed the entire transfer fee will be made available for new manager Ronald Koeman to reinvest: “We fought to ensure that we got the right deal for a player in whom we have invested a great deal of work over the past decade.”
“This deal is a good one for Southampton, and hopefully sends a clear message to other clubs wishing to bid for our players.”
“Luke’s transfer fee will be reinvested into the team as Ronald Koeman builds for the new season and for years to come.”