The 17-year-old has made four appearances for the Gunners this season and has been described by manager Arsene Wenger as "a great hope for the future".
"It's the biggest confidence boost you can have," Gnabry told Arsenal's official website. "Arsene Wenger is one of the greatest coaches in the world and I'm happy to be in that position. I try to give him back what he believes in me.
"Since the start of pre-season, it's gone very well for me. I've played in the Premier League and the Champions League, and of course that's a big step.
"I'm very proud. I always thought that in football it can go quick or slow, but I didn't expect it to happen so quick."
Gnabry joined Arsenal from Stuttgart in 2011.