The 24-year-old, who made 70 league appearances during his time at the SGL Arena, has agreed a three-year contract with Bundesliga rivals Hamburg.
And Ostrzolek took the chance to explain the reasons for his departure in a statement on Augsburg's official website on Tuesday.
"I had a wonderful time at FCA and I am grateful to the club, the fans and the city," he said. "But I beg you to understand that I want to go to Hamburger SV for a new challenge, because I believe that this is the right move for me.
"I wish FCA all the best and good luck in the future."
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