The Italian tactician has been confirmed as Napoli's new head coach, following the departure of Maurizio Sarri.
Sarri has been in charge of Napoli since 2015 and led his hometown team to second place in Serie A last season with a club record of 91 points.
Ancelotti has signed a three-year contract, replacing Maurizio Sarri at the Stadio San Paolo.
Earlier on Wednesday, Napoli president Aurelio de Laurentiis praised Sarri for his contribution to the club.
Ancelotti said that he had chosen Napoli despite offers from all over Europe and Asia as well as the Italy national coaching job.
The 59-year-old has been on Chelsea's radar as Conte's replacement for several months and his agents are reportedly expected to meet the Blues today to discuss a possible move to west London.
Napoli completed 4 factors behind Juventus within the Serie A title race after faltering late on handy the Bianconeri their seventh successive league success.
According to Sky Sports Italia, Zenit have invited the 59-year-old former banker to Russian Federation to see Saint Petersburg and their training facilities.
Juventus boss Massimiliano Allegri was among the first to welcome Ancelotti back to Italian football, tweeting: "Welcome back to Italy Mister Ancelotti!"
"Chelsea-Sarri: nothing has changed yet", Palmeri wrote on Twitter. Regardless of profitable the FA Cup final Saturday in opposition to Manchester United, Conte is anticipated to depart Stamford Bridge this summer time.
The Senegalese worldwide was arguably the finest centre-back in Italy and Europe's elite are already circling.