On 16 August 2015, Inter manager Roberto Mancini confirmed the club was forced to sell Kovačić to Real Madrid due to Financial Fair Play regulations.
Speaking during a press conference after a friendly against Greek club AEK Athens, Mancini said, "There are rules that have to be respected.
I don't think anyone wanted this to happen but we have the Financial Fair Play regulations to follow.
We're all sorry about it: myself, the president, the management and the players themselves."
Real Madrid also confirmed the transfer two days later, announcing Kovačić had signed a six-year contract with the club.
The transfer fee was €29 million, according to Inter's financial filing in the section Management Report (Italian: Relazione sulla Gestione).
On 19 August, Kovačić was unveiled as a new player by Real Madrid at the Santiago Bernabéu Stadium, where it was revealed he would wear the number 16 shirt for the club.
Kovačić became the fifth Croatian player, after Robert Prosinečki, Davor Šuker, Robert Jarni and Luka Modrić, to join Real Madrid.

Four days after his presentation, he made his debut as a 70th-minute substitute for Isco as Real Madrid began the Liga season with a goalless draw at promoted Sporting de Gijón.
He scored his first goal in an 8–0 home win over Malmö FF on 8 December 2015.
On 3 January 2016, Kovačić received a straight red card in a 2–2 draw at Valencia for a foul on João Cancelo.
Until the end of his first season with Los Blancos, he made a total of 34 appearances.
In the opening months of the season, he was used quite regularly by then Real Madrid manager Rafael Benítez, playing in almost every midfield position there is – sometimes central, sometimes wide, sometimes further forward.
However, after Zinedine Zidane replaced Benítez in early January, Kovačić's appearances became increasingly infrequent.
With the Frenchman preferring to use a very defined starting 11 whenever possible instead of the more specific-lineups-for-specific-opponents approach employed by his predecessor, there was little room for Kovačić.
He made eight appearances and scored one goal en Real Madrid's route to the 2015–16 UEFA Champions League title.

Kovačić scored his first Liga goal on 29 January 2017 in a 3–0 win over Real Sociedad.
He was a part-time starter when Madrid won the 2016–17 La Liga and the 2016–17 UEFA Champions League.

During the 2017–18 UEFA Champions League, Kovačić made six appearances when Madrid won their third consecutive—and 13th overall—UEFA Champions League title.
On 16 August 2015, Inter manager Roberto Mancini confirmed the club was forced to sell Kovačić to Real Madrid due to Financial Fair Play regulations. Speaking during a press conference after a friendly against Greek club AEK Athens, Mancini said, "There are rules that have to be respected. I don't think anyone wanted this to happen but we have the Financial Fair Play regulations to follow. We're all sorry about it: myself, the president, the management and the players themselves." Real Madrid also confirmed the transfer two days later, announcing Kovačić had signed a six-year contract with the club. The transfer fee was €29 million, according to Inter's financial filing in the section Management Report (Italian: Relazione sulla Gestione). On 19 August, Kovačić was unveiled as a new player by Real Madrid at the Santiago Bernabéu Stadium, where it was revealed he would wear the number 16 shirt for the club. Kovačić became the fifth Croatian player, after Robert Prosinečki, Davor Šuker, Robert Jarni and Luka Modrić, to join Real Madrid.
Four days after his presentation, he made his debut as a 70th-minute substitute for Isco as Real Madrid began the Liga season with a goalless draw at promoted Sporting de Gijón. He scored his first goal in an 8–0 home win over Malmö FF on 8 December 2015. On 3 January 2016, Kovačić received a straight red card in a 2–2 draw at Valencia for a foul on João Cancelo. Until the end of his first season with Los Blancos, he made a total of 34 appearances. In the opening months of the season, he was used quite regularly by then Real Madrid manager Rafael Benítez, playing in almost every midfield position there is – sometimes central, sometimes wide, sometimes further forward. However, after Zinedine Zidane replaced Benítez in early January, Kovačić's appearances became increasingly infrequent. With the Frenchman preferring to use a very defined starting 11 whenever possible instead of the more specific-lineups-for-specific-opponents approach employed by his predecessor, there was little room for Kovačić. He made eight appearances and scored one goal en Real Madrid's route to the 2015–16 UEFA Champions League title.
Kovačić scored his first Liga goal on 29 January 2017 in a 3–0 win over Real Sociedad. He was a part-time starter when Madrid won the 2016–17 La Liga and the 2016–17 UEFA Champions League.
During the 2017–18 UEFA Champions League, Kovačić made six appearances when Madrid won their third consecutive—and 13th overall—UEFA Champions League title.
Mateo Kovačić