The Dutchman had previously questioned whether it was too much for Rooney to lead the side after their recent friendly against Valencia, but he still stands by the 28-year-old England international.
"I think he wanted to show more than the utmost best to the public that he is Wayne Rooney, the new captain," Van Gaal is quoted as saying by BBC Sport.
"Then I said to him, 'Let it fly, let it fly.' It is more important how you perform and not the captaincy."
"I have asked him if he was already the captain before. He said yes. But I said now you are the official captain and there is a difference."
Rooney has worn the armband as a stand-in during his 10-year spell at Old Trafford, but Saturday's Premier League opener against Swansea City is the first time he will lead the team out as full-time captain.