Silva opted to leave Manchester City at the end of the 2025/26 season, after winning six Premier League titles and the UEFA Champions League under Pep Guardiola, and he joined Los Blancos on a two-year deal as a free agent.
A move to Madrid marks a new chapter for the 31-year-old, having previously played in his native Portugal, France and England, and his experience will be vital as Mourinho looks to hit the ground running back in the Spanish capital.
Silva has been backed for a key role with Mourinho - by his old national team boss Fernando Santos - and the former AS Monaco playmaker stated it was a chance he had to take ahead of the 2026 FIFA World Cup.
"Having played against Real Madrid many times, you feel the importance of the club, and how great it is to be here," Silva told Real Madrid TV.
"When Real Madrid came calling, it was impossible not to say yes. I didn't think twice. Being close to my family, near Portugal, in a very similar culture, it helps. But the dream of playing for the best club in the history of football - because their trophies prove it - is a privilege.
"Mourinho is a coach who means a lot to Portuguese football. Since I was little, I've watched his teams a lot, and he always puts Portugal's name at the highest level. I'm very happy to be able to learn from him."