Callejon travelled to Italy earlier this week to undergo his medical and the 26-year-old has now put pen to paper on a four-year contract with Rafael Benitez's side.
Neither club have officially confirmed how much the deal is worth but reports in Italy suggest Napoli have agreed to pay Real 10 million euros for the former Spain Under-21 international.
Napoli said in a statement on their website: "Napoli announce the outright purchase of Jose Maria Callejon, the 26-year-old forward who comes from Real Madrid."
Callejon came up through the youth ranks at Madrid but moved to Espanyol in 2008 without making a first-team appearance for the club. He then returned to the Bernabeu in 2011 on a five-year contract and made 87 appearances in all competitions under Jose Mourinho.
Benitez has already brought in Belgian winger Dries Mertens from PSV Eindhoven this summer as he reinforces an Azzurri squad that finished second behind Juventus under former coach Walter Mazzarri.