The Brazilian, who joined the Blues on a free transfer from Paris St-Germain in 2020, has made 151 appearances for the Blues.
He has won three trophies in that time, including the 2020-21 Champions League.
Silva, 39, says his love for the club is “indescribable”.
“Chelsea means a lot to me. I came here with the intention of only staying for a year and it ended up being four years,” he said.
“It is already hard saying goodbye in the most normal of circumstances but when there is a mutual love, it’s even harder. But once a Blue, always a Blue.”
Silva joined the club when Frank Lampard was manager and has since also played under Thomas Tuchel, Graham Potter and Mauricio Pochettino.
He has made 34 appearances in all competitions for Chelsea this season, including 25 starts in the Premier League.
The former AC Milan centre-back, capped 113 times by Brazil, says he hopes to return to Stamford Bridge in a new role in the future.
“I hope to leave the door open so that in the near future I can return, albeit in another role here,” he said.
