Stankovic won the treble with the club in 2010 and had a reputation for scoring outrageous goals, such as an effort from the half way line against Schalke in the Champions League.
"This is your 'Drago' speaking, with a sense of emotion but also with great pleasure. I don't know if I can find the right words to say goodbye and to thank you properly for everything you have given me, your affection, your trust and your honesty," he said.
"The last 10 years have been the best of my life. I have grown both as a man and, with immense joy, as a footballer.
"The thought that I won't be pulling on the Inter shirt anymore brings tears to my eyes but I've always been frank and the tears are real. Unfortunately, in life there comes a time when you have to move on and look forward.
"During my time in Milan I've played alongside some wonderful footballers and above all some wonderful people. It's hard to find the words to thank them all.
"It's been an honour to wear these colours and they will always remain on my skin. I'll never remove them; nobody can ever remove them."