The Leicester City legend joined Cremonese as a free agent after the summer market shut. Vardy, 38, is still catching up after missing preseason, but has scored twice already this term.
On signing Vardy, Giacchetta told Retesport: "It was a spur-of-the-moment situation, born amidst a lot of discussion. When you see Premier League players doing well in Italy, rather than some older player coming and doing well, after (Edin) Dzeko and (Luka) Modric returned to Italy, we thought about Vardy. At first, it seemed like a joke, but instead we managed to get in touch with him.
"He was immediately open to it, and we closed the deal, which generated enormous enthusiasm within the club and in the city. He's an icon of English and international football, and he has an incredible mentality.
"He fit in immediately, and the group respects him for the way he approaches himself and trains. We've sold over 2,000 Vardy shirts."