Sky Sports Italia and Gazzetta Dello Sport reported that the 30-year-old was seen waving to fans at the airport and was whisked away for a medical before signing a contract later in the day.
Sanchez will link up with Belgium striker Romelu Lukaku, a 65-million-euro ($73 million) close-season signing from Manchester United, who scored on his debut for Inter Milan on Monday.
Sanchez joined Manchester United from Arsenal in January 2018 but has scored just three Premier League goals in 32 appearances.
Antonio Conte's reign as Inter Milan’s coach got off to a perfect start with a 4-0 win over promoted Lecce on Monday.
Inter Milan last won Serie A in 2010 under Jose Mourinho, and have been remodelled by former Italy and Chelsea boss Conte, who replaced Luciano Spalletti after the Chinese-owned club finish fourth last season.
