The Italy global defender emerged as a surprise transfer target for Chelsea on deadline day and a deal has been completed.
Both deals were concluded in the final hours of the transfer window, strengthening a Chelsea squad that had looked thin early on this season.
Meanwhile, BT Sport pundit James Horncastle says the signing of the 25-year-old seems like a panic buy by the London club.
The full-back joined Torino from Atalanta in 2015 and made 29 Serie A appearances last season.
On Zappacosta, a statement on Chelsea's official website read, "Chelsea Football Club has today completed the signing of Davide Zappacosta from Torino".
Trump pledges $1 million for hurricane relief, White House says
Sanders said the President wanted reporters to help him decide which organization would maximize the impact of his funding. On Tuesday, the President's campaign asked supporters to donate to charities involved in the Texas recovery effort.
Trump pushes tax reform in Missouri
The administration and GOP lawmakers have set an end-of-year timeframe by which they expect the tax legislation to be completed. As a presidential candidate Trump suggested lowering corporate rates and lowering the rate for top earners.
These Android 8.0 Oreo Features Are Making Android Ecosystem Better
This is why it still isn't clear when will some of the users be able to upgrade their phones to the Android 8.0 O update. Android Oreo ( Android 8.0) update timeline for the HTC flagship smartphone announced.
The England global signed a five-year deal with Chelsea and adds experience to a thin midfield after multiple departures this summer.
Drinkwater played a big role in Leicester's incredible title-winning campaign of 2015/16.
Zappacosta becomes the fifth new addition for the Blues after Alvaro Morata, Tiemoue Bakayoko, Antonio Rudiger and Willy Caballero.
Both new signings will be in line for their Blues debuts following the global break and should be feature plenty with Chelsea's fixture list piling up toward the end of September. "I'm delighted to be a Chelsea player and can't wait to get started", said Drinkwater.
However, Drinkwater and Zappacosta should both prove to be good signings for Chelsea as they embark on their Champions League campaign, with both players excited to be along for the ride.
"I hope I can show my quality to the coach, my team-mates and the supporters", he added.