The Austrian forward only joined the Potters in the summer of 2013, penning a four-year contract upon his arrival from Werder Bremen.
He has adjusted quickly to life in England and has offered no indication that he is the difficult character he was portrayed as prior to his Premier League switch.
Recent displays have been so impressive that speculation of a transfer back to mainland Europe has surfaced, but Arnautovic has been quick to commit his long-term future to Stoke.
He said in The Sentinel: "Yes, I hope to be here for some years.
"I just arrived, so I cannot say I want to go in a minute.
"I like it here. I think the people have taken me into the group and helped me to settle in. I am happy to be here and the people are very friendly."
Arnautovic was acquired by Mark Hughes for his creative talents, but the 24-year-old says he has adapted his game accordingly to deal with the rigours of life in the English top-flight.
He added: "It is hard football here. People tackle a lot, but I like it and am happy.
"It is quick football here and it is the best league in the world. You have to deal with it.
"Before I came I didn't play too often in my other team, so my fitness was a little bit down and I think I needed one or two months to get it back.
"For me now it is okay. I think I can run the whole game and feel very fit."