Zappacosta has agreed a € 2.5 million-a-year deal for the next four years.
Torino confirmed the deal before Chelsea made it official, with the Premier League champions perhaps otherwise engaged as they also looked to get a late deal for Danny Drinkwater over the line.
Welcome, Zappacosta! May you have a Chelsea career as prolific as Frank Zappa's musical productions and as prolific as Diego Costa's goals.
Chelsea has made improvements to the side that won the league a year ago, but they have been beaten by other clubs for some of their targets during this summer transfer period.
Body of missing Dr
His umbrella was found near India Bulls in Lower Parel, giving rise to suspicions that the doctor may have fallen down a manhole. The Brihanmumbai Municipal Corporation (BMC), police and divers launched a search operation through Tuesday night to locate Dr.
"I hope I can show my quality to the coach, my team-mates and the supporters", said Zappacosta.
Technical director Michael Emenalo said: "Davide is a player of worldwide calibre who Antonio Conte knows well and we have been aware of for some time".
He has been frustrated during much of the summer transfer window, losing out on Alex Oxlade-Chamberlain to Liverpool and long-term target Fernando Llorente to London rivals Tottenham.
Zappacosta has signed a four-year contract with the Premier League champions and the Italy worldwide is delighted to have made the move, explaining playing for Chelsea in the English top flight is a dream come true.
Zappacosta is set to provide competition on the right flank at Stamford Bridge.