The Brazil defender ended his time in the French capital after PSG decided not to offer their captain an extension.
"I am so happy to be joining Chelsea," Silva said. "I am delighted to be a part of Frank Lampard's exciting squad for next season and I'm here to challenge for honours.
"See you soon Chelsea fans, I look forward to playing at Stamford Bridge very soon."
Chelsea director Marina Granovskaia said: "We are delighted to be able to add a player of Thiago Silva's proven world-class credentials to our squad.
"Having performed at the highest level for many years, we have no doubt his experience and quality will complement the many exciting talents we already have here. Thiago will be an excellent fit and we hope he can add some new trophies to his impressive list of honours."
The Brazil international's contract with the French club ended in June but he signed an extension that allowed him to play out the Champions League.
The 35-year-old is confident he still has three or four years of top European football left and turned down a two-year deal from Fiorentina to join the Blues.