The 62-year-old Holland coach has signed a three-year contract and will take over at Old Trafford following the World Cup finals.
"To manage the biggest club in the world makes me very proud," Van Gaal said.
"It was always a wish for me to work in the Premier League. 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."
United's second managerial appointment within a year, Van Gaal was approached by Tottenham Hotspur in the wake of André Villas-Boas' dismissal in December, however he will instead manage Britain's biggest club instead.
Van Gaal will be tasked with returning United to the top of the Premier League table after the deposed champions plummeted to seventh under David Moyes.
Ryan Giggs, interim coach for the club's final four games, could prolong his career in the player-manager role he occupied during Moyes' 10-month reign.
Frans Hoek is the Netherlands' goalkeeping coach, and Marcel Bout, an assistant coach to Van Gaal, will follow him to old Trafford.
Louis van Gaal
Giggs said: "I am thrilled to have the chance to serve as assistant manager. Louis van Gaal is a world-class coach and I know I will learn a lot about coaching from being able to observe and contribute at such close quarters. Manchester United has been a huge part of my life and I'm delighted to be able to continue that relationship in such a key role."
Enjoying his second stint as Holland coach, Van Gaal won three Eredivisie titles, the Uefa Cup and the Champions League with Ajax in the 90s, before succeeding Bobby Robson at Barcelona in 1997, where he collected two La Liga titles and the Copa del Rey.
A scarcely believable Eredivisie championship win with AZ Alkmaar in 2009 preceded a Bundesliga title with Bayern Munich, whom he led to the Champions League final in 2010.
Van Gaal faced Sir Alex Ferguson four times as a coach. Twice with Barcelona in 1998, as they and United played out two unforgettable 3-3 draws, and with Bayern Munich 12 years later, when they eliminated United from the Champions League quarter-finals on away goals.