The 51-year-old, whose contract expires in the summer, revealed before Sunday night's 2-1 loss at Roma that he would reveal his future plans once the season was over.
Reports in Italy suggest he could take the reins of conquerors Roma, who have been managed by Aurelio Andreazzoli on an interim basis following Zdenek Zeman's departure, while both Inter Milan and AC Milan are rumoured to be looking for new managerial blood.
Mazzarri told Napoli's official website: "The moment has come for me to reflect. Napoli is a marvellous place but I am leaving after four years because the players need some new stimulation.
"I've talked to the lads in the changing room and the president, I was emotional and I hugged everybody.
"I thank the fans... and all of those who've been close to me in these wonderful years.
"I took this decision some time ago. Out of respect, though, I wanted the players to be able to give their all right to the end, which they did."
Mazzarri, who previously managed Livorno and Sampdoria, arrived in Naples in October 2009 as a replacement for Roberto Donadoni and led the club to a sixth-placed finish in his debut season.
The Azzurri finished third in the following season to secure a place in the Champions League group stages for the 2011/12 campaign, where Mazzarri steered his men into the last 16 before their elimination by eventual winners Chelsea.
"I've taken Napoli as far as I can and I've put all my strength into this team and I think I have fulfilled the mandate in the right way," he added.
"I thank (president Aurelio) De Laurentiis and (director of sport Riccardo) Bigon who tried to change my mind, but I think it's time to go and sit still for a few months or even try a new challenge.
"It depends on the offers. Naples has a precious treasure and a solid club which is very healthy, and I think they will have a bright future."
Confirmation the Stadio San Paolo hotseat is soon to be empty feeds speculation that club president De Laurentiis could appoint a manager with Barclays Premier League and Champions League experience, with the names of Chelsea interim boss Rafael Benitez and former Manchester City manager Roberto Mancini circulating on the peninsula.
De Laurentiis later tweeted: "We salute Mazzarri for everything he has done. We turn the page and keep on growing. You will know who the new coach is through Twitter."