On 2 September 2013, Arnautović joined Premier League side Stoke City on a four-year contract for a fee of £2 million. He was assigned the number 10 shirt by manager Mark Hughes who also described his signing as a coup—"People will very quickly see what an outstanding talent he is. In terms of his power and his pace, which is something I think we need in the squad, he ticks all the boxes. Technically he's excellent and I'm really looking forward to working with him. I think it's quite a coup to get him here. It made sense to us and made sense to him that this is the right club for him. He's got a real desire to make an impression." Arnautović made his Stoke debut twelve days later in a 0–0 draw against Manchester City at the Britannia Stadium. After spending a month at the club, manager Hughes stated that Arnautović had adapted well to English football after being given a free-role in the side. On 26 October, he scored his first goal for Stoke, a 25-yard free-kick in a 3–2 defeat against Manchester United. Arnautović ended his first season in England with five goals in 35 appearances, and the team finished in ninth position in the Premier League.
Arnautović was born in Floridsdorf, a district in the northern part of Vienna, to a Serbian father and an Austrian mother. Arnautović is an Orthodox Christian. He is married to Sarah (née Lizakowski), and together they have two daughters, Emilia and Alicia. During his time spent in Italy and Germany, Arnautović developed a bad reputation with the media as "the bad boy of Austrian football". Speaking on the matter in October 2013, he admitted he was "not an angel" but insisted the birth of his daughter had made him "grow up."