The 41-year-old begins his stint at Milan on Monday, and spoke with the Italian press upon his arrival at Milan airport.
He said: "If you see my old interview that I gave, it is a club that is really special to me.
"It is a big challenge. I promised myself after the last one (Manchester United) that I would choose a smaller challenge.
"But I am here, and (the challenge) is even bigger."
Amorim's 14-month tenure at United ended in January 2026.
He managed 63 matches, with a 38.1% win rate, a record of 24 wins, 18 draws and 21 defeats.
Milan finished in an improved 5th position last season compared to an 8th placed finish in 2024/25, as Amorim looks to help his new club climb further up the table this time around while competing in the UEFA Europa League.