The 21-year-old German joined the Gunners' youth set-up in 2011, but has made just 10 Premier League appearances for the first team, while he had a brief loan spell at West Brom last season.
"I'm very happy to be here," he said. "I had very good talks with the management and that has lead me here to Werder and the Bundesliga.
"(Former Arsenal teammates) Per Mertesacker and Mesut Ozil have only said positive things about the club.
"I'm confident we'll have a successful season and push for the top half of the table."
Gnabry will be in the Bremen squad when their Bundesliga campaign resumes at home to Augsburg on Sunday, 11 September.