The former Werder Bremen striker made the switch last month.
"The trainer gave me a very good feeling about the club when he came over to Germany to speak to me," Arnautovic told The Sentinel.
"He said many good things and made Stoke City a very good option for me.
"I am really happy to be here and I have to thank the club for giving me this opportunity to come here and play in the Premier League.
"I hope that I can pay them back for the faith they have in me with good performances."
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