The 24-year-old, who has made eight appearances for his country this season, becomes the fourth new arrival under boss Mark Hughes following the signings of Erik Pieters, Marc Muniesa and Oussama Assaidi.
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A statement from the Potters read: "Stoke City are delighted to sign Austria international winger Marko Arnautovic from German side Werder Bremen.
"He joins on a four-year deal for an undisclosed fee."
Arnautovic moves to the Britannia Stadium for a reported fee of around £2 million, the fourth club of his senior career after spells with FC Twente, Werder and a season-long loan in Serie A at Inter.