The 25-year-old full-back has signed a four-year contract with the Red Devils with an option for a further one year.
“To work with Louis van Gaal, a manager that has achieved so much in football is such an exciting prospect.”
Darmian made his Serie A debut as an AC Milan player at age 17 in 2006 and has since featured for Padova and Palermo.
He scored five goals in 47 appearances in all competitions for Torino last season and made a total of 146 appearances for the Italian club.
The defender has 13 international caps for Italy and was part of their World Cup squad last summer in Brazil.
“Matteo will be a great addition to the team. I am delighted to welcome Matteo to the club and look forward to working with him in the coming days,” manager Louis van Gaal said.