Gnabry, 21, was promoted to the Arsenal senior side in 2012. Since then the youngster has played just 21 games for the club scoring just 1 goal. Last summer he was sent on loan to fellow English Premier League side West Bromwich Albion.
After joining the German side, Gnabry addressed the media and said:"I'm very happy to be here. Per Mertesacker and Mesut Ozil have only said positive things about the club.
"I had very good talks with the management and that has lead me here to Werder Bremen and the Bundesliga.
"The Olympics were a personal highlight for me and I'd like to carry on my development here at Werder Bremen.
"I'm confident we'll have a successful season and push for the top half of the table.
Serge Gnabry was a part of the German squad which took part at the Rio Olympics 2016. He had an impressive tournament with his national side.
A move to Bremen will be a great move in his career as Gnabry had very little chances of playing for the Gunners considering the array of quality midfielders they have.