The 34-year-old, a free agent since being released by Spurs after his contract expired in June, will undergo a medical at the weekend.
He was linked with moves to a host of top European clubs including Manchester United, Fiorentina and a shock return to Tottenham.
Llorente has scored 13 goals in all competitions for Tottenham, including crucial strikes against Borussia Dortmund and Manchester City during Spurs’ run to the Champions League final last season.
He returns to Italy, having played for Juventus between 2013 and 2015.
According toSky in Italy, Napoli has opted to sign Llorente after their effort to land Inter Milan outcast Mauro Icardi failed to materialize.