The Croatian player had an outstanding campaign in the World Cup, helping his nation reach its first final.
Modric was named the best player of the tournament in Russia, receiving the Golden Ball in recognition of his performances.
According to Sky Italy, the former Tottenham star had been seriously interested in a switch to Inter where three of her countrymen play.
Ivan Perisic yesterday published an image on social networks himself with Marcelo Brozovic and the recent addition of Sime Vrsaljko.
The winger, who has been courted by Manchester United, brazenly labeled Modric in the picture and said "Who is losing?" in his legend.
Zanka – Huddersfield were solid defensively last season, and the Dane was the top scorer of points in the back. He played in the World Cup and should be a key man again
But the Real fans will be relieved to hear the emergence that the 32-year-old has agreed a deal to stay at the Bernabéu.
According to Brand, Modric's salary increase will now be on par with captain Sergio Ramos and just behind Gareth Bale.
The salary increase is an indication of how important it is for the team and how valuable it is to him, the top brass of Los Blancos.
Modric seemed to be attracted by Inter's interest in Serie A in him, which is said to be a six-year contract offer.
The agreement would have consisted of four years in San Siro and two years in his Chinese brother club Jiangsu Suning.
The boss Luciano Spalletti publicly stated that he was "dreaming" with the club's supporters of the player's arrival at San Siro.
But the president of Real Madrid, Florentino Perez, was determined to hold on to Modric following the departure of Cristiano Ronaldo at the beginning of summer.
The supreme declared that the only way in which the midfielder would sell I was if his huge release clause of £ 676m was fulfilled.
Modric has won 14 trophies at Real Madrid, including the last three consecutive titles of the Champions League.