The 30-year-old was photographed waving to fans at the airport and was whisked away for a medical before signing a contract later in the day, Sky Sports Italia and Gazzetta Dello Sport reported.
Sanchez will link up with Belgian striker Romelu Lukaku — a 65-million-euro ($73 million) close-season signing from Manchester United — who scored on his debut for Inter on Monday.
Sanchez joined United from Arsenal in January 2018 but has scored just three Premier League goals in 32 appearances.
Antonio Conte’s reign as Inter coach got off to a perfect start with a 4-0 win over promoted Lecce on Monday.
Inter 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.
Inter travel to Cagliari in Serie A on Sunday.
