Daily Focus learnt that The 34-year-old wing-back has put pen to paper on a six-month contract with the Italian giants, with the option to extend this for a further season. He will wear the number 15 shirt.
According to mirror, the deal is subjected to the completion of a medical, which is due to take place on Friday.
Young was out of contract at Old Trafford in the summer and turned down the offer of a one-year extension to remain at United.
The former Watford and Aston Villa star will link up with former Red Devils pair Romelu Lukaku and Alexis Sanchez, who is on loan, in Italy.
Young made 261 appearances for the Red Devils from 2011 until now.
But the wing-back fell down the pecking order in recent seasons, and has this year lost his place in the first team to both Brandon Williams and Luke Shaw.
As things stand, Antonio Conte’s Inter are just two points behind league leaders Juventus.
Inter Milan have confirmed the signing of Ashley Young from Manchester United, with the wing-back linking up with former Red Devils pair Romelu Lukaku and Alexis Sanchez in Italy.