The Argentine keeper was released by Manchester City at the end of the season, and is understood to have agreed terms with Chelsea in order to become Asmir Begovic's replacement for next season.
The Citizens sealed the transfer of goalkeeper Ederson for £35 million, and Caballero received interest from Newcastle United or Boca Juniors, but finally decided to join Conte's side.
The 35-year-old is believed to have already passed a medical test and the signing will be confirmed in the coming days.