The 62-year-old, who has signed a three-year deal, will take charge of United when his role as Netherlands coach comes to an end after the World Cup.
Van Gaal has won multiple major trophies during his managerial career, which includes spells with Ajax, Barcelona and Bayern Munich.
"It was always a wish for me to work in the Premier League," the Dutchman told United's official website. "To work as a manager for Manchester United, the biggest club in the world, makes me very proud.
"I have managed in games at Old Trafford before and know what an incredible arena Old Trafford is and how passionate and knowledgeable the fans are. This club has big ambitions; I too have big ambitions. Together I'm sure we will make history."
Van Gaal will leave his position as Dutch national team coach this summer following a two-year stint in charge.