The 24-year-old becomes the fourth new arrival under manager Mark Hughes following the signings of Erik Pieters, Marc Muniesa and Oussama Assaidi.
The club said on their official Facebook page: "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."
The move for Arnautovic, who had a brief and troubled spell playing under Jose Mourinho when he was manager of Inter Milan, was reported to be worth around £2million.
Arnautovic follows Holland defender Pieters, Spanish centre-back Muniesa and Liverpool loanee Assaidi at the Britannia.
Winger Jermaine Pennant was also brought back to the club by Hughes having been released before the former QPR manager's appointment.
Pennant's free-kick against West Ham this weekend gave Stoke their second win in three games this season.
Source: PA
Source: PA