The Barclays Premier League club have announced that Van Gaal, current coach of the Holland national side, will take charge at Old Trafford after the World Cup with Ryan Giggs as his assistant.
Van Gaal, the 62-year-old former Ajax, Barcelona and Bayern Munich boss, has signed a three-year contract.
United executive vice-chairman Ed Woodward said: "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."
The vastly experienced Van Gaal was quickly identified as the club's top target after David Moyes was sacked in April.
The appointment of Giggs, 40, ends speculation over the future of the club's most decorated player. Giggs had served as interim manager for the final four games of last season.
Moyes, appointed only last year following the retirement of the long-serving Sir Alex Ferguson, paid the price for a poor season.
United, champions in 2013, could only finish seventh in the Premier League this year and therefore failed to qualify for European football.
Van Gaal will therefore inherit a squad that has slipped to a low ebb but he boasts a rich coaching pedigree and plenty of experience of handling big-name players.
He won three Dutch titles and the Champions League with Ajax in the 1990s before winning La Liga twice in charge of Barcelona. Further titles have followed, back in Holland with AZ Alkmaar and then in Germany with Bayern.
During his career he has also had two spells in charge of Holland, the second of which ends after this summer's World Cup in Brazil.
In January Van Gaal made public his desire to work in the Premier League.
He was linked with Tottenham but, due to his impending availability, he immediately became a favourite for the United job after Moyes' departure.
His ongoing work with the Dutch side meant discussions with the club took time, while the future of Giggs and other backroom staff was also thought to be a key topic of negotiation.
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."
Giggs is looking forward to the opportunity to work under Van Gaal.
The long-serving Welshman 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."
Woodward added: "I'm delighted that Louis has chosen Ryan as his assistant. Ryan's association with the club spans over two decades and his knowledge and stature will be of great use to Louis.
"In addition, this is a fantastic opportunity for Ryan to learn his trade alongside a world-class manager whose attacking instincts and belief in youth are tailor-made for Manchester United."
Van Gaal is thought likely to make a number of changes to the squad but some will be necessary anyway, notably in defence following the departures of Rio Ferdinand and Nemanja Vidic.
Club owners Joel and Avie Glazer are convinced Van Gaal is right man to take them forward.
Joel Glazer said: "I am delighted that Louis will be our next manager.
"He has an outstanding pedigree as a coach, both as a man who motivates his teams to win trophies and as someone who believes in giving young players a chance to prove their worth.
"I am sure he will make a big impression on the club, the players and the fans."
Avie Glazer said: "Louis joins us at an exciting time and has already communicated some great ideas for how the club can move forward.
"The board is right behind him in his plans and everyone here is already looking forward to the start of next season."
In addition to Giggs, Holland goalkeeping coach Frans Hoek and coach Marcel Bout, a specialist in opposition scouting, will join the backroom staff.
As yet there has been no announcement from United concerning the future of Moyes' former assistants Phil Neville and Chris Woods.