The Austrian forward is in contention to make his debut against Manchester City on Saturday and is relishing the prospect of playing in the Premier League.
Arnautovic is determined to make an impact and repay the faith shown in him by Hughes after the manager made a positive impression on him the first time they met in Germany.
"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."
While Arnautovic hopes to feature against Man City, he would understand if Hughes decided to ease him in with a substitute appearance.
He said: "It's a great game to start with because they are a very big team with many world class players, and if the manager decides to play me that would be great. But if not, that is no problem."
The 24-year-old added: "I don't like talking about myself as a player, but I am a technical player and I feel that I will fit in very well with the very good players who are already here, and with the style of play that the coach likes to use."