British media have said Shaw cost around 30 million pounds, eclipsing the 25.
6 million United paid to Everton for Wayne Rooney in 2004, a figure that would also make him one of the costliest defenders.
Shaw changed his Twitter profile on Friday morning to read: “Professional footballer at Manchester united Football Club” before quickly removing the information, but the transfer was confirmed later in the day.
“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,” he told the club website.
“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.”
The teenager, who was part of England’s doomed World Cup squad and earned his third cap in the goalless draw with Costa Rica, will compete for a place with experience Frenchman Patrice Evra, who himself signed a new one-year deal at United in May.
Shaw has penned a four-year deal with an option for a further year.
United missed out on the lucrative Champions League spot after finishing last season in seventh place in the Premier League. A series of limp displays also cost manager David Moyes his job before the end of the campaign.
Dutchman Louis van Gaal, still with the Netherlands in Brazil, has since been appointed and has been tasked with returning United to England’s elite as quickly as possible.
Herrera, 24, will bring some skill and vitality to a ponderous midfield, while Shaw, despite his young age, has made 60 Premier League appearances in two seasons and will offer competition and attacking instincts on the flank.
United have seen highly decorated defenders Rio Ferdinand and Nemanja Vidic leave the club as they look to move on from a poor season following the retirement of Alex Ferguson.
Ryan Giggs, who retired at the end of last season after managing the club following Moyes’s departure and will now assist van Gaal, said they were delighted Shaw was joining.
“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.”
Shaw’s departure is the latest blow for Southampton, who finished the Premier League campaign in eighth place with a club-record 56 points. Following the end of the season, manager Mauricio Pochettino left for Tottenham Hotspur while striker Rickie Lambert joined Liverpool.
Media reports on Friday said midfielder Adam Lallana, who also earned a spot in Roy Hodgson’s World Cup squad on the back of his strong club form, was set to have a medical ahead of a potential move to Liverpool.
Southampton, who have appointed Dutchman Ronald Koeman as manager following Pochettino’s departure, said after Lambert’s move that they had received a number of offers for players, but that they were under no pressure to sell.
“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,” Southampton executive director Les Reed said on the club’s Twitter account.
“This deal is a good one for #SaintsFC, 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.”
(Reporting by Josh Reich, editing by Pritha Sarkar)