Aurelio De Laurentiis was frustrated with his coach's refusal to sign a new deal with the club this summer amid speculation he might leave for England and has now confirmed Sarri is set to depart.
He tweeted: "I'd like to thank Maurizio Sarri for his valuable contribution to the Napoli cause.
"He brought joy and prestige to Naples and Napoli fans all over the world with an entertaining brand of football that drew praise from all quarters. Well done, Maurizio. Aurelio De Laurentiis."
Meanwhile, Antonio Conte is set to depart Stamford Bridge after Chelsea offered only a limp defence of their Premier League title and failed to finish in the top four. Although he won the FA Cup, beating Manchester United 1-0 in the final, he has a strained relationship with both the board and the squad.
His departure is set to open the door for Sarri to take charge.
The Blues, however, face competition over the 59-year-old Italian, who has also caught the eye of Zenit St Petersburg, who were willing to match the manager's release clause in order to lure him to Russia.
Sarri, who was named Italy's coach of the year in the 2015-16 season, saw his stock rise at the beginning of the campaign as his Napoli side raced to top spot in Italy's top flight.
However, they ultimately faded, and though they posted a club-record tally of 91 points this season, finished second in the standings behind Juventus, who won the title for the seventh successive season.
There had been a suggestion that he might have been willing to stay with the Italian side, but contract talks broke down and he will leave Napoli after three years in charge. He had previously spent time at eight different Italian sides, including Perugia, Hellas Verona and Empoli.
Carlo Ancelotti, who left Bayern Munich in the autumn, will replace Sarri having signed a three-year to deal to take over the club on Wednesday.
Meanwhile, Napoli stars Faouzi Ghoulam, Jorginho, Elseid Hysaj and Kalidou Koulibaly have all been linked with summer moves to the Premier League.