The Spanish international, 21, was officially unveiled as a Madrid player at a press conference on Wednesday afternoon.
Isco signed a five-year contract with Los Blancos on June 27.
"I want to thank the efforts of the president in bringing me here," he told reporters. "I have to say that for a player there is nothing bigger than being at Madrid, it is the best feeling, and I hope to enjoy myself here and make everyone happy here."
Isco was part of the Spain squad who recently won the Under-21 European Championship in Israel.