He took over as Arsenal manager in 1996 and has led them to a top-four finish in every season since.
Wenger has denied British media reports that Arsenal have offered him a new contract, but Gazidis indicated that the Frenchman would continue at the helm for the foreseeable future.
"The reason we have Arsene as our manager is because our board believes he can deliver success," he told the Daily Telegraph. "He is in fantastic shape. He is deeply engaged and excited."
"He is going to be managing us next year and we are planning and making many decisions for the long term."
Wenger, who last won the Premier League 12 years ago, faced hostility from the fans towards the end of last season.
"I know Arsene wouldn't stay on if he thought the club wasn't heading in a good direction and thought he wouldn't be able to deliver what the fans want," Gazidis said.
Arsenal finished second in the table last season, 10 points behind champions Leicester City.
(Reporting by Nivedita Shankar in Bengaluru, editing by Ed Osmond)
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