The defender signed a four-year deal with the west London club, while the England international agreed to a five-year deal with the English champions.
On Zappacosta, a statement on Chelsea's official website read, "Chelsea Football Club has today completed the signing of Davide Zappacosta from Torino. The 25-year-old can play at wing-back or full-back and has been capped by Italy. He has signed a four-year deal at Stamford Bridge."
Chelsea confirmed Drinkwater was their sixth and the last signing of the summer transfer window.
"Danny Drinkwater is officially a Chelsea player after today completing a transfer from Leicester City and signing a five-year-contract," a statement read.
Antonio Conte's men were intent on strengthening their squad throughout the summer transfer window but were made to wait until the very last day to bolster their ranks. The Blues boss stated his desire to add more depth to his title-winning squad on a number of occasions and, after a period of intense frustration, he has finally got his wish.
Zappacosta, a rather left-field signing, jetted into London from Rome and underwent a medical on Thursday (31 August) before completing his £25m move from Torino. The 25-year-old Italy international was not Chelsea's top wing-back target, but the Blues eventually saw fit to sanction a move after seeing Alex Oxlade-Chamberlain and Danilo join Liverpool and Manchester City, respectively.
Drinkwater was pursued by the Premier League champions for a number of weeks and attempted to force through a move a few days ago by submitting a transfer request at Leicester, who only gave him permission to undergo a medical with the Blues just a couple of hours before the 11pm deadline.
The England international will now provide competition with the likes of N'Golo Kante, Cesc Fabregas and fellow summer signing Tiemoue Bakayoko for a place in the Chelsea engine room, though he won't be joined in west London by his compatriot Ross Barkley, who reneged on a move to the champions in the dying moments.
Everton had agreed a deal worth £30m with Chelsea for the 23-year-old playmaker, who made no secret of his desire to leave his boyhood club earlier this summer, but the former Leeds United loanee reportedly changed his mind during his medical and has opted to remain at Goodison Park until January at least.
Barkley is not the only player to reject Chelsea's advances in recent days: Oxlade-Chamberlain chose Liverpool over the Blues after being promised game-time in a central midfield role at Anfield, while Fernando Llorente eventually opted to join Tottenham despite having a long-standing desire to ply his trade under former manager Conte.