Gattuso left Napoli last week after they failed to secure Champions League football on the final day of the season. The former AC Milan midfielder has since been appointed as manager of Fiorentina.
The Partenopei finished in fifth place following a 1-1 home draw with Hellas Verona, consigning them to another season of Europa League football.
Napoli were also knocked out of this season’s Europa League at the round of 32 stage by Spanish La Liga side Granada.
Gattuso joined Napoli in December 2019, replacing Carlo Ancelotti and led them to a seventh place finish in Serie A and a Coppa Italia triumph over Juventus.
In a club statement the club owner, Aurelio De Laurentiis, said: “I am delighted to announce that Luciano Spalletti will become Napoli coach on 1 July.
“Welcome, Luciano – we'll do great work together.”
Spalletti had been out of work after leaving Inter Milan in the summer of 2019.
The 62-year-old has also managed the likes of AS Roma, Zenit Saint Petersburg, Udinese and Sampdoria in the past.
He won two league titles with Zenit and a pair of Coppa Italia trophies while in charge of Roma.
