De Laurentiis posted a picture of him shaking hands with Benitez on Twitter with the message: "Rafa Benitez is the new coach of Napoli. A man of great international experience. A leader."
Benitez replaces Walter Mazzari, who left the club after their 2-1 loss at AS Roma in their last game of the season on Sunday and was on Friday appointed Inter Milan coach to replace the sacked Andrea Stramaccioni.
Mazzari took Napoli to second place in Serie A and re-established them as a force in Italian football. They also won the Italian Cup last season.
Benitez had been acting as Chelsea's interim manager since Roberto Di Matteo's sacking in November.
Under his stewardship Chelsea finished third in the Premier League and won the Europa League.
The 53-year-old has also had successful spells at Valencia and Liverpool before a disappointing six-month spell in charge of Inter.
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- Rafa Benitez