The 18-year-old left-back established himself as one of the hottest prospects in world football during his time at St Mary's, leading to admiring glances from many major clubs.
However, it is United that have won the race for Shaw's signature after he successfully passed a medical at the club's Carrington training ground on Thursday evening.
Shaw, who pre-empted United's official announcement by updating the bio on his Twitter page, has signed a four-year deal at the club.
Shaw said: "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."
United also signed Spanish midfielder Ander Herrera from Athletic Bilbao for £28.5m on June and have acted decisively in the transfer market so far - a stark contrast to their dealings last summer.
Shaw joins the club with aspirations of being first-choice left-back but Patrice Evra signed a new contract at the end of last season and will provide strong competition.
Manchester United assistant manager Ryan Giggs said: "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."
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