"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," the Serbian midfielder 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 34-year-old former Serbia international, who spent much of last season injured, won a host of trophies after joining the club in 2009, including five league titles, the Champions League and the Club World Cup. He was a key figure in the Inter side that won the treble in 2010.
He terminated his contract by mutual consent with Inter a year before it was due to expire.
"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."