Van Gaal, 62, has signed a three-year contract to succeed David Moyes who was sacked in April after a disastrous run of results.
His contract with the Dutch national side means van Gaal will not be able to join up with United until after the World Cup in Brazil, which would not be until mid-July if the Netherlands reach the latter stages of the tournament.
Van Gaal, a disciplinarian who has won domestic titles and cups with Ajax, Barcelona and Bayern Munich as well as the Champions League, will become the first manager from outside the British Isles to take charge of United.
He quickly emerged as the favourite to take over at Old Trafford after Moyes was dismissed.
Giggs, United’s record-appearance holder and a player-coach under Moyes, was placed in caretaker charge of the team after the Scot left Old Trafford.
Moyes was the handpicked successor of former United manager Alex Ferguson after his compatriot retired as British football’s most successful boss at the end of last season.
But the former Everton manager struggled to adjust to life at Old Trafford and was dismissed just months into a six-year contract after United failed to qualify for next season’s Champions League.