Gnabry started his professional career with Arsenal, making his debut back in 2012, and his move to Bavaria may now actually help his former club as the German giants may drop their interest in Alexis Sanchez.
He said of his move: "It is a great honour to be part of FC Bayern. It's going to be an exciting time and one that I'm very much looking forward to", he told Bayern's official website.
Bayern chairman Karl-Heinz Rummenigge said, as quoted by the club's website: "We're pleased that in Serge Gnabry another young German worldwide is coming to FC Bayern".
"We are delighted to see another young German national player in FC Bayern in Serge Gnabry", Rummenigge said.
Serge Gnabry has made a decision to leave Werder Bremen after just one season at the club.
Gnabry failed to cement a place in the first team at Arsenal in four seasons at the Emirates Stadium, spending the 2015-16 season on loan at West Brom.