The former Juventus striker returns to Italy following the expiry of his contract with Tottenham.
Llorente, 34, spent two seasons in north London, scoring two Premier League goals and three in the Champions League, including the controversial effort which earned Spurs a semi-final triumph over Manchester City in April.
The former Athletic Bilbao, Sevilla and Swansea City centre-forward previously scored 16 times in a title-winning Serie A campaign for Juve.
Napoli have not confirmed the length of the deal, but reports in Italy indicate it is for two years.
Llorente's move to Stadio San Paolo could herald the end of the club's reported interest in Inter star Mauro Icardi, who has been told he can leave.
Carlo Ancelotti's men have scored eight goals in their two matches this term but lost 4-3 to defending champions Juve in their final outing before the international break, Kalidou Koulibaly's late own goal settling Saturday's thriller.