The Spanish midfielder has returned to his homeland after his decade-long spell at Manchester City came to an end.
Italian side Lazio had been confident of signing the 34-year-old but he has opted to return to La Liga.
Silva became a City legend during his time at the club, which came to end after Pep Guardiola's side were eliminated from the Champions League by Lyon.
City have announced that they intend to honour Silva with a statue outside the Etihad Stadium.
Silva won 13 honours at City and thanked the club in a social media message on Monday (17.08.20).
He wrote: "The time has arrived. Ten years and 13 titles later, it's time for me to say goodbye to the club that has left an indelible mark on my life and career.
"I look back and it's clear I could not have made a better decision than to accept City's proposal to join their project back in 2010.
"Manchester City and I have grown together. In 10 years, I have developed personally and professionally. I have celebrated many victories and titles and lived through epic moments.
"Precisely because of that I want to tell you it has been a real pleasure wearing the sky blue shirt and the captain's armband of our club, sharing the dressing room with the best players and coaches in the world, and working closely with the finest club representatives and board members the game has to offer.
"I hope that City will achieve even bigger triumphs in the future. I am going to support the team from a distance. I am so happy I have shared these unforgettable moments with the City family - you will always be in my heart."