The 31-year-old did not get anywhere near the heights expected by the Old Trafford faithful after joining from Arsenal in January 2018 in a deal which saw Henrikh Mkhitaryan go the other way.

Having scored just five goals in 45 appearances, Sanchez spent the 2019-20 season on loan at Inter Milan - a period in which United covered a hefty portion of his wages.

Although the Chile international scored only four goals in Italy's top flight this season, he seems to have rediscovered his touch in Italy and provided eight assists as Antonio Conte's side finished runners-up behind Juventus.

Sanchez has done enough in Serie A to secure a permanent move, bringing an end to an uninspiring stint in the north-west of England.

"FC Internazionale Milano announce that Alexis Sanchez has joined the Nerazzurri on a free transfer," the Italian club said in a statement on Thursday.

"The Chilean forward has signed a permanent contract with the club until 30 June 2023."

The PA news agency understands United made a small pay-off to Sanchez but as he had two years left on his mammoth deal, ending his stay early means they avoid paying a reported Stg40 million ($A73m) in wages.

Figures at Old Trafford are believed to be satisfied with the conclusion to the situation and the club publicly sent their best wishes to the departing forward.

"Everyone at Manchester United wishes Alexis Sanchez all the best in his future career as he joins Inter Milan on a permanent transfer," a United statement said.

The transfer will also allow Sanchez to play for Inter in the Europa League after they advanced to the quarter-finals on Wednesday with a 2-0 win over Spanish side Getafe in Gelsenkirchen, Germany.

Inter CEO Giuseppe Marotta on Wednesday announced that a deal with Sanchez had been agreed.

"The player is completely ours and we have a three-year contract with him," Marotta told Sky Sports.

"We think he can be a full member of our squad."

Australian Associated Press