The Croatian winger returns to Inter less than a month after completing a treble-winning season in Germany.
Perisic capped off his successful stint with a Champions League winners medal after appearing in August's final against Paris Saint-Germain, which Bayern won 1-0 in Portugal.
He played in 22 league matches - scoring four goals and providing six assists - as Bayern charged toward their eighth consecutive Bundesliga title in June.
Perisic also appeared in the DFB-Pokal final to help Bayern beat Bayer Leverkusen.
His current deal at Inter runs until 2022, but there's uncertainty as to whether he has a future at the club under manager Antonio Conte.