The Spanish attacker has signed a four-year deal with the Serie A club, and brings his second stint with his boyhood club Real Madrid to a close by agreeing to the move.
The 26-year-old made 40 appearances under Jose Mourinho at the Santiago Bernabeu last term, but will now hope to help his new club build on their second-place finish in the Italian top flight.
Callejon began his career with los Blancos' C and B teams, after graduating from the club's youth academy, but after growing frustrated at a lack of first-team opportunities in the Spanish capital, he moved on to Espanyol in 2008.
His time at the Catalan club was the most successful of his career up until that point, as he made 106 appearances over three seasons, scoring 12 goals.
That form convinced Madrid to bring him back to the club for a fee of £4.7m, and the forward would go on to play a prominent role in their 2011-12 title-winning campaign.
He has now opted to take on a new challenge, however, and will link up with Napoli as they begin life under new boss Rafael Benitez.