The 21-year-old scored 11 goals in 27 Bundesliga appearances to help Werder to eighth place in the table having made the move from the Emirates Stadium last summer.
However, he has now triggered a clause in his contract which allows him to leave the club at the end of the month, and the player himself confirmed that his career will continue "elsewhere".
"Werder Bremen are indeed a special club and have surpassed my expectations. I was handed the chance to prove myself here and I am very thankful for it," Gnabry wrote in a post on Instagram.
"But my path will continue elsewhere. And I will reveal where another time. Today, it's important to me to say Thank You! I will keep Werder in my heart."
Bremen sporting executive Frank Baumann added: "Serge has told us that he wants to make the next step in his career following his very good first year at Werder. He therefore will trigger a release clause and leave the club at the end of this month."
Reports in Germany suggest that Gnabry will join Hoffenheim following their qualification for the Champions League, while RB Leipzig, Borussia Dortmund and Bayern Munich have also been credited with an interest.