Arnautovic spent last season on loan at Inter, but failed to secure a permanent move.
The 21-year-old has now signed a four-year contract with Werder Bremen.
“We are pleased that it was possible to reach an agreement with FC Twente after good negotiations,” explained Werder Bremen sporting director Klaus Allofs.
“Marko Arnautovic has great potential. We trust him with a good role in our team.”
“Werder are very successful working with young players. I see a great opportunity to take the next step in my career,” said Arnautovic.