Earlier on Saturday, the Blues confirmed that they had appointed Maurizio Sarri as their new manager for the next three years following the sacking of Antonio Conte on Friday.
Goal understands Chelsea will pay £57m (€65m/$86m) for the player, with Jorginho having signed a five-year contract with the club, where he will earn £102k per week.
Speaking to the club's official website, Jorginho said: "I am absolutely ecstatic to be here at Chelsea. It is not easy to become part of such a big team so I am very, very happy.
"I am excited to play in such an intense league, for a team that gives everything to play and win."
The Italy international was an important member of Napoli's squad under Sarri and the Blues expect him to have a similar influence in London.
"We are delighted Jorginho has chosen to join Chelsea," club director Marina Granovskaia said. "He was one of the most coveted midfielders in Europe and will become an important member of the playing squad.
"He has demonstrated his quality working under Maurizio Sarri and we are convinced his signing will help bring further success to Stamford Bridge."
City were previously interested in the 26-year-old Italy international but it is Sarri's side who have won the race to sign the player.
Indeed, it had been expected that the midfielder would join up with the Premier League champions, who also had a five-year deal on the table less than a fortnight ago.
"We are talking about a lad for whom Manchester City represents the opportunity of a lifetime."