Giggs took temporary charge at Old Trafford towards the end of last season after David Moyes was relieved of his duties.
The Welshman won two games, drew one and lost another before being handed the role of assistant manager when Van Gaal was appointed.
He is clearly excited about the prospect, too, having talked up his new colleague - who will attempt to turn around a team that finished seventh in the Premier League last season.
In quotes published on the club's Twitter feed, Giggs said: "He won't be afraid of taking over. He'll relish it. He has a clear philosophy and he sticks to that.
"I got a taste in the dugout last season and I'm looking forward to working with Louis.
"He's been at huge clubs, but in my view this is the biggest. It's tough to win the league but that's what we'll try to do."
United have also revealed they will take on Valencia in a pre-season friendly at Old Trafford on August 12, just days before the new season begins.
Giggs added: "It will be a good introduction to Old Trafford for the new manager and new players."
Van Gaal will first take charge of his new club in the United States, where they are set to face LA Galaxy, Roma, Inter and Real Madrid.
