The Manchester United manager - then in charge of the Netherlands - was preparing for his side's semi-final clash with Argentina when he analysed footage of Rojo.
And Van Gaal is delighted to have the chance to coach the player, who completed a £16 million move from Sporting Lisbon earlier this week.
"I played him in the World Cup against Argentina, so I had to analyse Argentina," he said.
"[From] that video I was already enchanted about him because my philosophy is you have to buy players who fit in the profile, and I think Marcos fits in the profile as a left central defender but also as a left wing back.
"He played a fantastic World Cup, so I am very pleased."
"I'm very happy to be here at the biggest club in the world," he said. "It's a great honour.
"It [the transfer] was a little bit of a long process, but the most important thing is that I'm here now and ready."
"I've received messages from all of them: 'Congratulations and welcome to Manchester'," he added. "We know each other outside of football as well."
On the subject of the potential departure of striker Danny Welbeck, Van Gaal added: "I know what I said to Danny and Danny knows exactly what I said to him. That is private."
