The Portuguese midfielder, who arrives on a free transfer from Manchester City, spoke to Real Madrid TV afterwards with his excitement clear.
"It's very special and I'm very happy to be here. There's no need to talk about this club, because its whole history speaks for itself," he said, before putting himself at the team's service:
"I'm very happy to start and try to help this team keep winning, which is what it knows how to do. I'm one more player here to help and try to continue this spectacular club's path of victories."
On his first training sessions, he acknowledged the physical toll but praised the group's atmosphere.
"Tired. The first training session was tough, but I'm very happy to meet my team-mates. Some of them I already know quite well because I played against them many times," he explained. "The people here have really good intensity, and this place feels like home."
He also reflected on Mourinho, whom he faced as a rival in the past.
"We've been rivals a few times and now we're on the same side. He's a coach who means a lot to Portuguese football; since I was little we watched his teams a lot, and he's always put the name of Portugal at the highest level. I'm very happy to be able to start and learn with him."
Asked what he could bring to the squad, he described himself as a versatile, team-first player.
"I'm a hard-working player, someone who tries to make the players around me better. I always try to be available in various positions to help the team. I can fit in many places and I'll be ready for whatever Real Madrid needs."
Silva explained that the call from the club left no room for doubt, and that he said yes without hesitation.
"When Real Madrid came calling, it was impossible not to say yes, I didn't think twice," he admitted. "Having played against Madrid so many times, you feel how big it is to be here, how imposing the Bernabéu is. Being close to my family, very close to Portugal, in a very similar culture, helps. But the dream of playing for the best club in the history of football is a privilege."
Finally, he named his footballing influences, one of whom is now tied to the club he has just joined.
"I have many, and Zidane, without a doubt, is one of them. Also Rui Costa, for being a Benfica and Portugal player, and Modrić, who has been a huge reference and an example both on and off the pitch," he stated.
"Zidane is perhaps top five in the history of football. He played more or less in my position, and when I was a kid, I watched how he controlled the ball and how he played."