The new deal will keep the highly-rated Uruguay international at the club until the summer of 2016.
Cavani joined Napoli from Palermo on a one-year loan deal last summer, but the move has now become permanent.
De Laurentiis told Radio Marte: “With Edinson we met today and we have extended our relationship. Then he left for Uruguay after signing the new agreement with me.
“We are satisfied and I am personally pleased to have a champion in the team but especially a nice person. Edinson is a man who has great faith and great personality, an important element for a Napoli team that has plenty of personality.”
