The Roma striker has joined the Rossonero in an initial loan deal.
At today's presentation, Abraham said: "I grew up with Milan. I think they are an excellent team. I am often asked how I want to play. I am always ready to face new challenges. I hope to have good results, to have a positive impact, we have the wind in our sails.
"When I saw Milan were interested in me, I did nothing but wait, telling myself a thousand times that this was the place I wanted to be.
"I feel great. I'm recovering from the injury, but I feel really good.
"I grew up with this club, in my heart and soul, with all the trophies and players, playing here, in this fantastic city and in this fantastic stadium, as are the fans. I would like to contribute with my best. I will try to make the season go as well as possible."