The England left-back has signed an initial four-year-contract at Old Trafford after the two clubs agreed on a fee for the 18-year-old, who also becomes the third most expensive defender in the world behind Paris Saint-Germain's Brazilian pair David Luiz and Thiago Silva.
Shaw became the youngest player at the World Cup with his appearance against Costa Rica
Shaw, who had been capped by England at U16, U17 and Under-21 level before his senior debut against Denmark earlier this year, was part of Roy Hodgson’s squad for the World Cup earlier this summer.
And after arriving home from Brazil on Wednesday, United moved quickly to secure Shaw’s signature by agreeing terms with Southampton, where the Kingston-born defender came through their renowned youth academy.
He travelled north on Thursday for a medical, while the finer details of the deal were completed between the two clubs before the transfer was completed on Friday afternoon.
"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," Shaw told ManUtd.com
"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."
Shaw, who was the youngest player to appear at the World Cup in Brazil after starting Tuesday's game with Costa Rica, becomes United’s second new signing in two days following the arrival of Spanish midfielder Ander Herrera from Athletic Bilbao on Wednesday.
With new boss Louis Van Gaal appointed for the 2014-15 campaign, Shaw will be hoping to add to the 60 top-flight appearances which he has already made with the Saints.
