The 37-year-old joined the Blues from Paris Saint-Germain in 2020, initially on just a one-season deal.
However, he has become a key figure as Chelsea won the Champions League last season and sit second behind runaway leaders Manchester City in the Premier League.
“To play here with Chelsea is a real pleasure. I never thought I would play for three years here in this great club, so I’m very happy to stay for another season,” Silva, who has made 56 appearances over the last 18 months, told the Chelsea website.
“I’m going to give everything to keep playing at this level in the most important league in the world.”
Tying down the Brazilian international to an extended contract has become a priority for Chelsea with fellow centre-backs Antonio Rudiger and Andreas Christensen also out of contract at the end of the season.
“Thiago Silva’s experience, leadership and performances have been and remain very important to this squad, so we are hugely pleased to extend his contract by another year,” said Chelsea director Marina Granovskaia.
“We look forward to his continued influence as we seek honours this season and next, and more of the qualities that have led to him having such a big impact for us on and off the pitch.”