Van Gaal will formally take over after Holland’s World Cup campaign is over this summer.
Ryan Giggs will stay on as the Dutchman’s assistant, having taken over in temporary charge following David Moyes’ sacking.
United confirmed the appointment on Twitter, with the 62-year-old revealing his delight.
“It was always a wish for me to work in the Premier League,” said Van Gaal, who signed a three-year-contract.
“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.”
Frans Hoek and Marcel Bout also join United as assistant coaches, but there is no place for former Holland striker Patrick Kluivert.
A statement from Old Trafford read: “Louis, 62, has managed at the top level of European football for over 20 years and in that time has won domestic titles and domestic cups in three countries, as well as the UEFA Champions League, the UEFA Cup, an Intercontinental Cup, two UEFA Super Cups and domestic Super Cups in Holland and Germany.”
United executive vice-chairman Ed Woodward added: “In Louis van Gaal, we have secured the services of one of the outstanding managers in the game today.
“He has achieved many things in his career to date and Old Trafford provides him with a fitting stage on which to write new chapters in the Manchester United story.
“Everyone is very excited about this new phase in the club’s history. His track record of success in winning leagues and cups across Europe throughout his career makes him the perfect choice for us.
“People know him as a larger than life character but I have also been extremely impressed by his intelligence, thoughtful approach to the role and his diligence. I’m looking forward to working with him.”