The left-back, who joined from Chelsea, was candid about what triggered his decision. A personal call from José Mourinho was the turning point.
"When a coach like Mourinho calls you, it's something to be proud of," he said.
"He messaged me first and then called. When he calls and tells you things directly — that's important.
"I can't wait to start working with him. I'm at a great moment in my career and I really want to play for Real Madrid."
Cucurella acknowledged the weight of the move. He knows what the club demands and says he is ready for it.
"It's a huge challenge. Every player at Madrid is good. Fitting in isn't easy. You have to be at 100% in every game. Every team wants to beat you."
His arrival creates an interesting dynamic on the left flank. Vinícius Júnior is his direct partner, a player not always known for tracking back. Cucurella is unbothered.
"I think we'll understand each other well," he said. "I don't care if he doesn't come back. I'll do everything he doesn't want to do. As long as he's decisive and fresh to score goals, I'll handle the dirty work. Vinicius has shown he's a decisive, influential player in Madrid's Champions League wins."
There is also the matter of his former Chelsea teammate Enzo Fernández. Reports have linked the Argentina international with a summer move to Madrid, and Cucurella made clear where he stands.
"He's a great player and a friend," he said. "He congratulated me on the signing. Hopefully it happens. We've been very happy at Chelsea and the chance to both sign for Madrid in the same summer would be something. Hopefully he gets lucky and becomes a Real Madrid player."
Cucurella also addressed Spain's performance so far. The draw against Cabo Verde prompted a group response.
"We were really annoyed because we knew we hadn't started well," he said. "The wake-up call did us good. We realised that if you're not at 100% you can go out early. I think it's been useful."
He pointed to the return of Lamine Yamal as a factor in Spain's improvement.
"He's growing a lot as a person and as a player over these past two years since the Euros," he said. "He arrives much more mature. If you look at his age he's still a kid — but already a man. Age is just a number and I see him as very mature."
On the draw in the bracket, Cucurella played it straight. "I don't look at the draw much. The most important thing is to focus on ourselves. At the Euros, we had the hardest draw — and look how it ended."