The centre-back, 35, moves to Stamford Bridge on a one-year deal. The Blues also have the option to extend the player’s contract by another 12 months.
Chelsea had been closely linked with Silva, who played his last game for Ligue 1 title-winners PSG earlier this month in the Champions League final defeat by Bayern Munich, and the Brazil international joins Timo Werner, Hakim Ziyech and Ben Chilwell as another high-profile signing by the Premier League side this summer.
“I am so happy to be joining Chelsea,” Silva told the club’s official website.
“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.”
Silva joined PSG in 2012 and went on to captain the side, winning seven Ligue 1 titles in his eight years at the club. He also lifted the Coupe de France trophy five times and the Coupe de la Ligue trophy on six occasions.
The news of Silva’s move comes a day after the Blues announced they had secured the services of 21-year-old defender Malang Sarr, who left Nice at the end of last season.
Sarr, who primarily plays at centre-back, joined Chelsea on a five-year deal, though he will spend the upcoming season out on loan.
Before that, former Leicester left-back Chilwell completed his move to Stamford Bridge on Wednesday for a fee reported to be in the region of £50million.
Chelsea coach Lampard has been keen to make defensive reinforcements as a result of his team’s weakness at the back last term.
The former Blues midfielder has also improved his side’s attacking options, however, with the signings of striker Werner from RB Leipzig and winger Ziyech from Ajax, while Bayer Leverkusen midfielder Kai Havertz is the final key target for the club in this window.
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