The club made the announcement at a news conference on Friday where flamboyant president Aurelio De Laurentiis initially made out that Cavani was moving to Manchester City.
"At times marriages come to an end. Unfortunately Edi wants to go to England, to that cold city of Manchester, and there's a plane ready to take him there," said De Laurentiis as he sat alongside a giggling Cavani.
Cavani then signed his new Napoli deal in front of the media.
"I thank the president who has believed in me and enabled me to remain in this amazing city," the 25-year-old striker said.
"Every time I go out on the pitch I want to win. That's my mentality and that of the team."
De Laurentiis said Cavani had a release clause of 60 million euros ($75.63 million) in his new contract.
The Uruguayan had been linked by media reports with moves to City and European champions Chelsea.