The Spanish frontman has been available on a free transfer after his contract with Spurs was not renewed at the end of last season.
Llorente has had an agreement in place with Napoli for some time, but the Serie A giants were looking at other strikers, including Inter’s Mauro Icardi, before settling for the Spaniard.
A two-year contract has been agreed between the player’s representatives and Napoli ahead of his transfer, reports Sky Italia.
The Spaniard will report for a medical over the weekend before signing before the deadline on Monday..
Tottenham wanted to retain his services and even offered him a one-year deal to continue in north London.
But Llorente, who was short of playing time at White Hart Lane, is thought to be keen on more first team action.