Gunners boss Arsene Wenger has high hopes for Gnabry, who has been capped by Germany at youth level.
Gnabry has already made an impression for the Gunners' first team - scoring in the 2-1 victory at Swansea earlier in the season, a week after making his full Premier League debut against Stoke.
He made the step up to during the 2012/13 campaign, making substitute appearances in the Premier League at Norwich and the Champions League home match against Schalke
Wenger told the club's official website: "We signed Serge Gnabry because I believe that he will be a great player.
"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 Football Club."
Gnabry admits he is delighted with the new deal as well as the opportunities that have already come his way at Arsenal.
He said: "Arsenal is a great football club and I'm so happy to be here and sign a new contract. For me, now it's all about working hard and developing my game.
"I've had some good opportunities recently in the first team, which has given me extra confidence, and this will only improve my game. I'm looking forward to giving my best for this club in the years to come."