Silva, 35, has agreed to an initial one-year contract with the Premier League club, who have the option of extending the deal by a further season.
I am so happy to be joining Chelsea. I am delighted to be a part of Frank Lampard’s exciting squad for next season and I’m here to challenge for honours,” Silva told Chelsea’s website.
“See you soon Chelsea fans, I look forward to playing at Stamford Bridge very soon.”
Silva’s eight years in Paris ended with the 1-0 Champions League final defeat against Bayern Munich in Lisbon last weekend.
The former AC Milan centre-back represents a departure from Chelsea’s usual protocol of focusing major signings yet to reach their peak.
But Lampard moved quickly to bolster a defence that conceded more Premier League goals than any other team in the top 10.
Silva won seven Ligue 1 titles with PSG and will be expected to provide experience and leadership at the heart of Lampard’s defence.
“We are delighted to be able to add a player of Thiago Silva’s proven world-class credentials to our squad,” Chelsea director Marina Granovskaia said.
“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.”
Silva is the latest new arrival at Stamford Bridge as Lampard rebuilds a side that finished fourth in the top-flight last season, 33 points behind champions Liverpool, and lost the FA Cup final against Arsenal.
Lampard has already signed Leicester left-back Ben Chilwell, Leipzig striker Timo Werner, Ajax playmaker Hakim Ziyech and former Nice defender Malang Sarr.
Chelsea are also expected to sign Bayer Leverkusen forward Kai Havertz shortly in a £90 million ($119 million) deal that would take their total spend in the summer window to a Premier League record £230 million.
Lampard’s new recruits could make their debuts in Chelsea’s Premier League opener at Brighton on September 14.