The France international has joined Milan on-loan with an option to buy next June.
Discussing his two years with Chelsea, Nkunku said: "I got injured straight away and was out for five months, and upon my return I had a relapse.
"In my second year, I worked hard and did everything I could to be ready, and the coach made his choices. I'm the same player I've always been, I want to play with a smile, and I know it will be different here in Milan.
"When AC Milan called me, I didn't have to think about it too much; I immediately knew it was the perfect option for me."
Nkunku also stated: "I feel good. I was already working on an individual level, but I've started training with the team these days. I can't wait to get started with all my teammates.
"The first step is to get to know my team-mates, build bonds with them and with the coach, and at the end of the year we'll see where we've got to.
"I'm competitive, I know what I want and I always try to be the best version of myself. I can give a lot to this team, I like to move as an attacking midfielder but it all depends on the formation and how it's interpreted. The coach will decide, I can't wait to play."