The Chilean has spent the last year on loan at the San Siro and was desperate to quit Old Trafford.
Sanchez made the switch from Arsenal to United in January 2018 in a move that made him the Premier League's highest paid player.
Inter were never going to be able to match his current pay packet and the Red Devils have still been paying a substantial amount of his wages.
But the drop in pay will see the 31-year-old lose out on £1.2m a month.
Sanchez has signed a three-year deal with the Nerazzurri and will earn £200,000-a-week.