The 35-year-old joins Frank Lampard’s side on a one-year contract after leaving Paris Saint-Germain following their Champions League final heartbreak by Bayern Munich.
Following his arrival, Silva told the club’s official website: ‘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. See you soon Chelsea fans, I look forward to playing at Stamford Bridge very soon.’
Chelsea director Marina Granovskaia then hailed: ‘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.’
Thiago Silva becomes Chelsea’s fifth arrival of the summer after the signing of Hakim Ziyech (£38m), Timo Werner (£53m), Ben Chilwell (£50m) and Malang Sarr (free).
