The 26-year-old becomes Chelsea’s sixth signing of the transfer window.
Djilobodji was in the final year of his contract at Nantes. The defender has signed a four-year contract at Chelsea.
Djilobodji said: “I’m very happy to sign for a big club like Chelsea and I want to do my best to help the team win titles.
“I want to thank the club for giving me this opportunity.”
.@ChelseaFC is delighted to announce the signing of Papy Djilobodji from Nantes… http://t.co/1lHKPD2XFf pic.twitter.com/4kca7uI7d7
— Chelsea FC (@ChelseaFC) September 1, 2015