The Brazil international joined the French side from AC Milan before the beginning of the 2012/2013 season.
Silva quickly became one of PSG’s most important players, having led the club to their seventh Ligue 1 trophy in eight seasons, and 23 trophies since he donned the iconic jersey.
PSG have turned down the opportunity to extend their captain’s contract and Chelsea are said to be in pole position to secure his services.
The Brazilian has agreed terms with the Premier League side and will sign a deal at Stamford Bridge until the summer of 2022.
Silva took to his Instagram account to bid an emotional farewell to the team from the French capital.
“The value of things is not in the time that they last, but in the intensity with which they occur. That is why there are unforgettable moments, inexplicable things and incomparable people,” wrote the centre-back.
“Today a cycle is ended, after eight years at PSG, I would like to thank my team-mates, the entire coaching staff and board, the fans, my family, God and my friends, for all of the happy years we have spent in the City of Light.
“Here, together with my wife, we have enjoyed unforgettable moments, our children grew up, we became French citizens, and we will carry forever in our hearts these years lived in France. Thank you so much.”