Di Maria completed his British transfer record £59.7 millon move to Old Trafford on Tuesday and has been handed the iconic No.7 shirt by the club.
The Argentine could make his debut against Burnley on Saturday but Van Gaal has warned fans not to expect too much too soon.
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"We cannot expect him to be the miracle after two of three days of training. We have to be the miracle. You have to work for the miracle and he knows that."
The Dutch boss has been on the look-out for players to fit his specific requirements all summer, and he believes Di Maria's versatility will be key to what he is trying to do at Old Trafford.
"He fits in our philosophy... he played in Real Madrid not only as a wide player but also in the centre of midfield," he added. "That is why we are convinced he will succeed."
"He will be a player who enjoys defence, and that's also a reason we have chosen him. But when you see him, you see that he is a very modest guy, he wants to work, he showed that also last year, he played 52 matches and he gave 22 assists.
"How many players can say that? Twenty-two assists! He is a very social human being and in the football world that is not always the case, as you know."
Van Gaal revealed that United are keen to further strengthen his squad before the transfer deadline on Monday, adding that some of his current squad leave.
He said: "The club will [announce] when the time's there," said the Dutchman. "Players will leave, others will come."