The 18-year-old German forward, who has made five appearances for the Gunners this season, penned a long-term extension at the Emirates Stadium on Monday.
Wenger believes that Gnabry is capable of making a big impact on the team in the future.
"We signed Serge Gnabry because I believe that he will be a great player," he 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 Football Club."
Gnabry made his first-team debut for Arsenal last season.