The 25-year-old is highly-rated in Italy having made his worldwide debut last year.
Zappacosta has been with Torino since joining the club from Atalanta in 2015 and he's been capped four times by the Italian national team having previously played for the under-21s. Sky Sports claims that the Blues will pay £23m, plus add-ons, for the 25-year-old.
Zappacosta has agreed a € 2.5 million-a-year deal for the next four years. And just like Alonso, he is yet another unexpected purchase from the Serie A who seems to have the potential to grow into a useful member of the squad.
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He is also relishing working under countryman Antonio Conte.
Reports suggest if Zappacosta were to be sold to Chelsea, than Torino would have to find another right-back in the transfer window as they would lack any cover in the position, apart from Lorenzo De Silvestri.
"I hope I can show my quality to the coach, my team-mates and the supporters", said Zappacosta.
Chelsea were close to signing Alex Oxlade-Chamberlain from Arsenal, having agreed a fee in the region of £40m for the English global, before the 24-year-old had a change of heart and decided against moving to the Stamford Bridge outfit.