The 19-year-old expressed his excitement at the opportunity to join the capital city club and claimed they were the only team he considered.
"This is the most important day in my life as I arrive at a club I've dreamt about since I was a child," he said as he gave a speech.
"There is no better Kings' Day present.
"When I decided to leave Manchester City I contemplated three options.
"The first was to play at Real Madrid, the second was the play at Real Madrid and the third was to play at Real Madrid.
"I didn't want to go anywhere else.
"He went on to speak of the responsibility he feels and the gratitude he has for those who made the move possible.
"I understand the responsibility that there is to give my soul for this club," he said.
"That's a non-negotiable thing.
"I want to express thanks for the confidence placed in me and thank my family for the efforts they've made during my personal and footballing development.
"Many thanks to all, and Hala Madrid!"
The winger signs on a six-and-a-half-year deal and will wear the No.21 shirt.