The Turkey international will make the switch at the end of the month.
“I am very happy, being at Inter is a big deal," he told Inter TV after committing to a deal to 2024.
“It's a great team, great club, great atmosphere and great fans. I know what it means to come here, it's a strong sensation.
“We want to win the Scudetto, just like last season."
Milan were top of the table at the midway stage, but Inter surged out in front to take the Serie A title.
“My first year in Italy was very difficult for me, as I didn't speak the language. I learned and made many friends in the city of Milan, including off the field.
“I played very well with Stefano Pioli in the last year, as I was able to play in my role.
“I prefer to provide assists rather than score goals, as I don't have that egotism of wanting to score at all costs. The team comes first.
“I want to bring quality and quantity. I know that I have to work hard, because nobody just gives you a starting shirt. If you suffer and work hard, you will always get your chance."
Calhanoglu revealed he spoke with former Inter star Emre ahead of making his choice.
"We talked about it, he said good things about Inter, that you work well here and are organised in every area. He told me Inter is a great club and I should enjoy myself."
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