Modric was the Spanish club's one main target throughout the summer and he feels that the Croatian has the ability to become a local hero after joining from Tottenham Hotspur.
"He was the only signing that we focussed on and we finally signed him which pleased me greatly," Mourinho told AS.
"I am sure that he will fit straight in to the squad and that the supporters here will really take to him. He has talent and tactical discipline in equal measure.
"Modric is a team player, who plays for the common good, and looks for and finds his team-mates.
"He also has a great touch, a bit of magic, that they will love at the Bernabeu. We signed Modric for Madrid because we will enjoy having him and he will help us win."