De Bruyne, 33, arrived in Italy on Thursday and met with Napoli owner Aurelio De Laurentiis after being mobbed by fans.
After 10 years with Man City, the Belgium international said he is confident he can still play at the highest level, and will now join up with Belgium team-mate Romelu Lukaku.
Napoli, who won their second Serie A title in three seasons last month, announced De Bruyne's arrival on social media, stating, "Kevin is proud to be one of us!"
De Bruyne won 19 trophies with City, including six Premier League titles and the Champions League, making 422 appearances and recording 108 goals and 177 assists.