The 19-year-old Ivory Coast international arrived from RB Leipzig in a deal reported at €125 million plus a further €15 million in add-ons, making him the most expensive signing in Real Madrid's history.
He has been training with his new team-mates for several days but has yet to feature in a pre-season fixture, missing out on Wednesday's Trofeo Teresa Herrera against Deportivo La Coruna after being left out of Mourinho's travelling squad.
Diomande said he was grateful for the welcome he had received at Valdebebas and eager to contribute as soon as he is given the chance.
"I'm grateful to be here and I want to share my happiness with everyone. I want to be part of the team's triumphs," he said, before crediting his manager directly for making the move happen.
"I want to thank the coach, because we had a conversation before and I'm here thanks to him and the club, of course.
"I'm happy. Thank you for this signing, and thank you to the club and the coach for believing in me."
That conversation with Mourinho is understood to have been decisive in persuading the winger to choose Real Madrid over Paris Saint-Germain, with the Portuguese coach reportedly speaking to Diomande in fluent French to talk through his ideas for the team and where the youngster would fit in. Diomande, who admitted to being naturally reserved in front of the media, was direct when asked about turning down interest from elsewhere.
"You can't say no to Real Madrid when they call, it's as simple as that, it's the best club in the world."
The winger, who signed a seven-year contract running until 2033, said he was already looking to soak up knowledge from a dressing room that includes Kylian Mbappé, Vinícius Júnior and Jude Bellingham.
"It's incredible, it's always good to have great players in the dressing room, you learn from them," he said, recalling watching many of his new team-mates on television before now sharing a changing room with them. Diomande also acknowledged the step up in demands he now faces at the Santiago Bernabéu compared with his time in Germany.
"It's different. This is tougher. That's normal, because it's the biggest club. You need to work harder than at other clubs to be the best in the world. And that's what I'm trying to do."