Cavani has signed on a five-year-deal, the club president Nasser Al-Khelaïfi confirmed, with the player revealing his joy at his move from Napoli.
He said: "This is a club that is among the top global and can fight for the Champions League.
"I come with a lot of joy, confidence and desire."
He added: "Ibra is a world champion. It is a pleasure to play alongside him to win titles."
Cavani made 33 appearances for Napoli last season, scoring 29 goals for the Serie A outfit.
The 26-year-old recently spoke of his unhappiness at comments the Napoli president made about him amid the summer speculation.“Edinson Cavani has been a long-term Chelsea target”
He said: "I love Naples. It's my town and my heart is there.
"But when I was here in Brazil I've heard untrue rumours and things about me.
"We must clear ourselves. I'll talk with him, as it's done between men, really soon."