The 35-year-old has signed a one-year contract at Stamford Bridge, with the club holding the option of an additional 12 months.
Here, the PA news agency highlights five things you may not know about the Brazil international.
His career was almost ended by illness
Silva initially moved to Europe in 2004 when he joined Champions League holders Porto from Juventude. He was loaned to Dynamo Moscow a year later but never played a game for the Russian club after suffering chest pain and being diagnosed with tuberculosis. He subsequently spent around five months in hospital. Doctors even considered removing part of his lungs during the lengthy illness, which would have ended his career long before he became a household name.
He hopes to emulate Paolo Maldini's longevity
After rebuilding his career back in Brazil with Fluminense, Silva moved to AC Milan in the 2008-09 campaign. His arrival at San Siro coincided with the final season before retirement of club great Paolo Maldini. Silva, who turns 36 next month, has previously described fellow centre-back Maldini as one of his idols and expressed a desire to match his former team-mate's achievement of playing professionally until the age of 40. "I will follow his path and my body will tell me if I am able," he said in 2016.
He was insulted by Joey Barton
In 2013, Marseille loanee Joey Barton was disciplined and later apologised for calling Silva an "overweight ladyboy". Barton, borrowed from QPR by the Ligue 1 club, made the controversial remarks on Twitter. The jibe was thought to be in response to provocative comments in French newspaper L'Equipe in which PSG man Silva spoke about an English player at Marseille, whose name he claimed to have forgotten, who had been criticising top players because nobody was talking about him.
He missed Brazil's humiliation at the hands of Germany
Germany's 7-1 semi-final thrashing of hosts Brazil in 2014 goes down as one of the most remarkable moments in World Cup history. Like the humiliated home fans in floods of tears, captain Silva was forced to helplessly watch the embarrassment from the stands. He was suspended for the high-profile match in Belo Horizonte after collecting a needless yellow card in the quarter-finals for deliberately preventing Colombia goalkeeper David Ospina from kicking the ball out of his hands.
He met 'Alex from Glasto'
Last year, Silva made time to meet Somerset teenager Alex Mann, who went viral after singing about the Brazilian on stage at Glastonbury. Mann, wearing a PSG shirt with 'Silva 2' on the back, was selected from the festival crowd to perform the song 'Thiago Silva' alongside British rapper Dave. Silva and 15-year-old Mann later watched the impromptu rap together while sitting in the Parc des Princes dugout. Silva's new Chelsea team-mate Mason Mount was quick to tweet a video of Mann following the completion of the transfer on Friday.