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."
Rojo is equally happy to have finally completed his move to Old Trafford.
"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."
Rojo also revealed he had received messages from his compatriots at local rivals Manchester City, who include Sergio Aguero, Martin Demichelis and Pablo Zabaleta.
"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."
Manchester United visit Sunderland in the Premier League on Sunday.
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
