The Uruguayan passed his medical on Wednesday morning before joining the rest of the squad for the first session of pre-season at Valdebebas. He shared his early impressions of the new project with Real Madrid TV afterwards, reflecting on both his relationship with the club's new head coach and the significance of inheriting the captaincy.
On working with Mourinho for the first time, Valverde said: "I'm looking forward to being able to learn from him, to listen to every piece of advice he gives me and to get the most out of every second or minute of every training session I get to share with him and his coaching staff.
"I'm going to try to learn, to grow as a person and as a footballer. He's a special person who I can learn a lot from. Hopefully it will be a great season."
On taking on the armband for the first time, he added: "I feel a lot of emotion and a lot of honour. Whenever someone stops me in the street or within my circle and says that to me, it really does fill you with pride and emotion.
"You think about everything that's happened - good things, bad things... and now the moment has come to be first captain. I learned a lot from all the team-mates who have been captains here. They've always given me incredible help, and I'm going to take all of that on board to grow alongside the coaching staff too."
Valverde also pointed to the influence of some of the club's recent leaders as he prepares to take on the responsibility himself.
"I grew up a lot with those players I got to share so many years in the dressing room with, like Dani (Carvajal), Sergio (Ramos), Toni (Kroos), Luka (Modrić) and Lucas Vázquez... I'll never get tired of naming them. They're players who have helped me a lot to grow as a person, as a captain and as a player. This is the first year I'm going to try to enjoy myself and give my maximum effort - not just on the pitch, but off it too, so that all my team-mates feel comfortable."
Looking ahead to the new campaign, Valverde said the collective goal was clear.
"Not just me, but the whole team - what we want most is to win trophies this year, for Madrid fans to be happy, to be able to enjoy a year full of titles, and for them to be proud of us."