Cavani pledged to stand by the Partenopei despite interest from Europe's top clubs and his 63m buy-out clause.
"I hope to stay here for a long time. I am enjoying this moment and everything that surrounds football in this city, such as the fans who give us an extra boost.
"Naples has given me so much and that is why I am so happy here. The warmth and affection of the fans have given me extra confidence. I have a great deal of love for them and for this city.
"My children are Neapolitan, as they are indelibly linked to this city, because they give me everything and I try to give something in return.
"I am the person you see. I am very quiet and have always relied on my belief in God. My faith is a reference point for me.
"I enjoy every day as if it could be my last. We are expecting another child, Lucas, who will join Bautista. Some players like to go out partying, but I like the quiet life.