The 25-year-old Italy international is poised to become United???s second signing of the summer, following the earlier arrival of Memphis Depay, and a four-year contract has reportedly been agreed.
Darmian is to join for a fee of around ??13m and has already written a letter to the Torino fans thanking them for their support.
And Torino coach Giampiero Ventura has given the move his backing, saying the club can use the funds acquired to try and build a stronger side.
Named the Italian national team???s best player of 2014, Darmian has just completed another fine season in Serie A for Torino, making 32 appearances.
He began his career with AC Milan before moving on to Palermo, and then joining Torino in 2011.