Napoli and Chelsea have reportedly agreed a £50m deal which will also see Jorginho receive £7m in bonuses.
Manchester City were also interested in the player, but were beaten to the deal by Chelsea.
According to Sky Sports, Jorginho was ready to snub City because he wanted to live in London.
It is unclear whether Maurizio Sarri had anything to do with the completion of the signing, but it is a possibility.
Antonio Conte's sacking was announced on Friday morning, and Sarri could soon be officially appointed as the new head coach.
Throughout the deal, Manchester City had believed they were in pole position to close the signing.
Jorginho reportedly told City a couple of months ago that he wanted to join them and move to Manchester.