Van Gaal officially started work as United boss last week after leading the Netherlands to third place at the World Cup and he oversaw a 7-0 thrashing of LA Galaxy in his first match on Wednesday night.
The Dutchman has enjoyed success at the likes of Ajax and Barcelona earlier in his career, and has been charged with the job of breathing new life into United following last term's lacklustre campaign under David Moyes.
Giggs has been named as van Gaal's assistant and the former United midfielder has been impressed by how quickly he has settled in.
"I do think there are similarities with Fergie," said Giggs. "They do have an aura about them. That comes from the success they have had.
"They demand the players respond and they demand respect.
"His CV speaks for itself. He has managed at big clubs and he is coming into the job off a successful World Cup so already, recently, he has shown what he can do.
"The players have responded to that. In the short space of time I have worked with Louis you can see why he has been a success.
"He is infectious. He wants everything right from the first minute of training to the last.
"Everything he does is clear, and everyone gets it straight away. He has got a unique way of putting it over but it's brilliant to see it at first hand.
"It's quite simple but if you make a mistake he will tell you and if you do something good he will tell you. You know what you are doing wrong and you know what you are doing right. He makes no bones about who you are."
Meanwhile, Giggs has called on the United players to restore pride in the coming campaign after last term's seventh-placed Premier League finish ensured there will be no European football at Old Trafford this season.
He added: "There's no doubt that few players lived up to the standards of what they are capable of doing last season.
"They are not bad players. They are all good players. It doesn't change overnight but last season's league position showed that we didn't perform individually or as a team.
"The way back for them has started already, in training. There is no time to waste.
"The World Cup means that some don't have much time to prepare but the recovery has to start now, getting some kind of form going into the Swansea game.
"The players have got to take a bit of pride in how they perform, train and play."