Van Gaal succeeded David Moyes in May but the Dutchman was not officially unveiled to the media until last week due to his FIFA World Cup commitments with the Netherlands.
The 62-year-old oversaw his first training session on Thursday before flying out to the United States for the club's pre-season tour.
Speaking ahead of United's opening International Champions Cup fixture against Los Angeles Galaxy on Wednesday, Van Gaal expressed his pleasure with the players' response thus far.
"I have to say that it has been fantastic," Van Gaal told reporters at the Rose Bowl Stadium.
"Maybe you think every coach who is new should say that but I mean it. They are anxious to follow the instructions of my assistants.
"The focus I have seen in the training sessions is top-level but we have to see if the performance is top-level.
"But I am very happy with the labour of my players in the days I have been with them."
United's trip to the USA, which will also pit them against Roma, Inter and Real Madrid, is a chance for Van Gaal to assess his playing stocks before adding to the signings of Ander Herrera and Luke Shaw.
Van Gaal wants to give all his players a chance to prove themselves, including striker Javier Hernandez, who was out of favour last season and has been linked with a move away as a result.
"I have to see if he performs how I want," said Van Gaal.
"Now I can only see what he has showed under the guidance of another coach.
"He will arrive this evening and I will meet him, we will train and after that he will perform in a match and then I can say something about that."
Van Gaal also refused to comment on transfer targets, with the reportedly pursuing Juventus midfielder Arturo Vidal and defensive duo Mats Hummels and Thomas Vermaelen.
"I want to learn about my players, to know them and when I give the orders, I want to see how they perform," he added.
"That is why I cannot answer this question now. I want to give all the players a chance to show themselves under my guidance."
United kick-off their Premier League campaign against Swansea City on August 16.
