The 18-year-old, who joined from Stuttgart in 2010, has enjoyed a breakthrough season at the Emirates Stadium this term with five outings.
|9/2||Serge Gnabry is 9/2 with BetVictor to score v Chelsea in the Capital One Cup|
"We signed Serge Gnabry because I believe that he will be a great player," Wenger told the club's official website. "He's nearly there now, and competes for a regular place in the team in the Premier League.
"He has technical ability, he has power, he has pace, he has finishing quality and he can give a final ball. He's a powerful offensive player and I believe that he will be a great player for Arsenal."
Gnabry has represented Germany at Under-16 to Under-19 level.