On Wednesday, the Red Devils unveiled Schweinsteiger, Schneiderlin and Matteo Darmian to the media in Seattle, where they are preparing for the first game of their pre-season tour against Club America at CenturyLink Field on Saturday.
Van Gaal often bemoaned his lack of balance in midfield last season and was forced to put captain Wayne Rooney in a holding midfield role on multiple occasions.
After signing Schneiderlin and Schweinsteiger, the Dutchman is confident he now has the balance he covets.
“I have already said in previous press conferences that my selection was not in balance and I have already mentioned in that period last year that I want to make the balance with midfielders,” Van Gaal said.
“So you could expect that I shall buy two holding midfielders. Now Morgan Schneiderlin is the type I think can play in our system and in our philosophy.”
Darmian was unable to say much at the press conference due to his limited English, but Van Gaal was more than happy to outline why he wanted the Italy international at Old Trafford.
“I want always a player who can defend in the first place,” Van Gaal said. “When you are a right full-back, you have to defend and you have to cooperate with your fellow defenders.
“What I have seen in Darmian is he has a very good orientation. With that orientation, he can cooperate with our central defenders because he has to close the space when the ball is at the other side.
“He is fast. He is also a reasonable header so that is also a plus and he can build up, he can see the free man.
“In an attacking way, he is a good player and Manchester United wants to attack with the full-backs.”
Despite praising his new signings, Van Gaal was keen to stress that nobody can be guaranteed a place in the United side this coming season.
Van Gaal said: “Every player who is sitting here can make that contribution but they know already they have to fight for their position.
“Never in top sport is it secure. No position is secure. Even my position is not secure, as you know.
“Morgan Schneiderlin has to fight with Michael Carrick, Schweinsteiger and Daley Blind. These are the players who can play in the centre of midfield.
“Matteo Darmian has to fight with (Antonio) Valencia.”
The United boss also admitted he is curious to see how Schweinsteiger and Darmian, who unlike Schneiderlin have never played in the Premier League, adapt to the physical nature of English football.
“Morgan can cope with the Premier League,” Van Gaal said. “The question mark is with Bastian Schweinsteiger and Matteo Darmian, because they have to prove it.
“That is the difference. There is a big difference between all the leagues and I have trained in them all, so I can judge that.
“But I am fully confident that Bastian and Matteo can cope with the rhythm of the Premier League.”
Van Gaal was keen to stress in the press conference how pleased he was that, unlike last season, United have concluded these signings before jetting off on tour and praised executive vice-chairman Ed Woodward for getting them completed in time.
“The difficulty is to get these players,” Van Gaal said. “It is not so easy. I am very pleased that Ed Woodward has done that.
“Memphis Depay is here and now the three new signings so it is much better than last year.
“It is not so easy when Manchester United is coming. They are always asking more money than you think you have to spend. But still they are here at the right time.”