The 26-year-old Spaniard signed a four-year deal with the Serie A side on Friday for a reported fee of £8.6m.
"Leaving Real Madrid is never easy, but for me Napoli is a really important step," Callejon told the club's official website.
"Benitez's call convinced me. This is a big club with international level, and I think we could show it in the Champions League."
Callejon scored five goals in 38 games for Madrid last season.