The highly rated 18-year-old, who this week became the youngest player to feature at the 2014 FIFA World Cup when he played in England's final group game against Costa Rica, has penned a four-year deal at Old Trafford with the option of a further year.
Shaw's arrival, for an undisclosed fee reported to be around £30 million, follows the capture of Spanish midfielder Ander Herrera, who joined United from Athletic Bilbao on Thursday to become the club's first signing since Louis van Gaal was appointed as manager.
Netherlands coach Van Gaal will begin his new role after the World Cup and can now count on the services of a teenager who has earned widespread praise since breaking into Southampton's first team in 2012.
Shaw, heavily linked with Chelsea as well as United, turns 19 next month, but has already made 60 Premier League appearances after coming through the youth system at St Mary's Stadium.
His departure continues a worrying trend for Southampton, who have seen manager Mauricio Pochettino and striker Rickie Lambert move on to Tottenham and Liverpool respectively following a season in which the south-coast club exceeded expectations en route to an eighth-placed finish in the Premier League.
Shaw told United's official 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."
United assistant manager Ryan Giggs welcomed the arrival of Shaw, who boasts three England caps.
"Luke is a very talented young left-back with great potential," added Giggs.
"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."
