Van Gaal was confirmed as United's new boss on Monday afternoon, signing a three-year deal with the former Premier League champions.
Giggs, who announced his retirement from playing professional football following Van Gaal's appointment, believes that he will be able to learn a lot from the Dutchman.
"I am thrilled to have the chance to serve as assistant manager," the 40-year-old told the club's official website. "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."
Van Gaal will take charge at Old Trafford when his role as Netherlands coach comes to an end after the World Cup.