The 62-year-old, who has agreed a three-year contract at Old Trafford, will take charge of the club after his deal with Holland expires at the end of this summer's World Cup.
Speaking about the news, Glazer described Van Gaal as a manager with an "outstanding pedigree" that is known for "giving young players a chance to prove their worth".
"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," he told the club's official website.
"I am sure he will make a big impression on the club, the players and the fans."