Milito has along with teammate Thiago Motta agreed a move to San Siro for next season.
Milito wrote in an open letter on the Genoa website: “To all you Genoa fans I want to open my heart and my mind to tell you what I’m feeling in this special day.
“First of all I apologise for not being able to celebrate with you all in Piazza della Vittoria, as the call for Argentina’s World Cup qualifiers mean I must leave early. So this letter will try, if possible, to tell you how much I care for you.
“I would like to look you all in the eye and embrace you in what is a see you soon, not a farewell. I said it when I returned here from Spain: Genoa is my home.
“I think it will remain so even after I stop kicking the ball. With you all, to this city, these people, this shirt, a bond that goes beyond professionalism ties me.
“I played football in many cities and different countries. Everywhere I was happy and wrote pages of my career, but never the way I have in my three seasons at Genoa.
“I wish to thank first of all who took me to Italy as a young player and wanted me again a year ago. Without them I wouldn’t be the player, nor the man, I think I am now.
“Thanks to Coach [Gian Piero] Gasperini and the staff, to the whole squad that fought, cried and celebrated together in taking Genoa to Europe after 17 years.
“I confess I returned because I strongly wanted this team and this city, but I found far more. The club had grown, was more organised and professional with a great future ahead of it.
“Thanks to the fans, young and old, who greeted me like a friend, like one of you. Certain moments with you will always remain in my mind as a man, not just a player. My son will grow up with the Genoa values that I practically have tattooed on my skin.
“Now we leave each other, I hope with a smile and affection that has become love, at least that’s what I feel. I go with the bitterness that characterises all departures, but the relaxed knowledge I leave Genoa where they deserve to be and where I want to see them every year.
“In the life of a professional, there are moments in which reason must prevail. My heart and emotions tell me to thank you once again. This is an ‘arrivederci.'”