The Torino star was subject to interest from Inter earlier in the window, but reports emerged in Italy on deadline day that the west London club had emerged as a candidate to sign him. Now Antonio Conte's side are close to their fifth signing of the summer.
Zappacosta is expected to sign a four-year deal and Chelsea could pay an additional £4.5 in add-ons for the 25-year-old Italy international.
The Blues will feel a sense of relief after missing out on several targets to strengthen their wing-back position. The Stamford Bridge side saw a £35m bid accepted by Arsenal for Alex Oxlade-Chamberlain, only for the England international to snub them and join Liverpool on Thursday.
Chelsea also missed out on Alex Sandro and Danilo earlier in the transfer window and most recently made an approach to sign Rafinha from Bayern Munich.
Chelsea continue their negotiations to add Leicester City's Danny Drinkwater after their most recent £32m offer for the midfielder.
WHO IS DAVIDE ZAPPACOSTA?
Zappacosta is among a group of talented Italian right-wing backs – also including Alessandro Florenzi and Andrea Conti – who are excellent going forward but less comfortable defensively.
The 25-year-old is extremely quick and fit, and is known for his lung-busting runs up and down the flank. He is a direct runner and likes to attack the full back and whip in a cross into the box.
He has shown his best in a 3-5-2 system to date due to his attacking qualities and ability to cover the whole flank. He is less adept in a four-man defence as he is not a natural defender. He can be caught out positionally and when it comes to defending his penalty area, particularly from crosses. Last season he was part of one of the worst back fours in Serie A alongside Joe Hart as Torino shipped 66 goals in 38 games.
However, with Antonio Conte favouring a 3-4-3 system, he will not have to worry so much about defending his area and he certainly has the physical and technical attributes for the Premier League. Given how much Victor Moses and Marcus Alonso improved under Conte, don’t be surprised if Zappacosta proves a shrewd acquisition also.