Mbappe has managed seven goals and one assist in eleven competitive matches for Real so far this season.
"We all know what a class player (Mbappé) is, he is one of the best in the world. To have him here today is a great satisfaction, it is a joy to share the pitch with him," Valverde told France Football.
"I have suffered (by playing against him) with PSG, and by playing against France with my country (Uruguay). He stands out in every match, in every practice. He is a top player. Thank God he is here with us. I can enjoy him, my family too, and my kids can watch him."
Valverde believes that Mbappé killed the rumours that his arrival could create friction between the team's stars.
"As a person (Mbappé) is incredible. He has silenced many people. (People said that) if he came here, there would be a lot of conflict, and I don't know what," he says.
"He has silenced all that, all those rumours, and he has shown that he is a spectacular person... (His Spanish) is impressive, better than mine!"