A sculpture of the Dutchman, who scored 120 goals and won three league titles in 11 seasons in north London, will sit outside Emirates Stadium alongside those of Thierry Henry, Tony Adams and Herbert Chapman.
Bergkamp said: "First of all, I am honoured that this is going to happen. It makes me very proud. Everyone knows that I love Arsenal and that I had a fantastic time at the club.
"For me and my family it was an important period in our lives. Next to that the people were great, the team was amazing and we had a lot of success over the years.
"I will do everything I can to be there when it will be unveiled. It will definitely be a special moment for me which I don't want to miss."
Arsenal chief executive Ivan Gazidis said: "It will be a fitting tribute to Dennis' huge contribution to the club that a statue will be on display outside Emirates Stadium in the near future.
"Dennis' quality and style of play will never be forgotten. He is a true legend of Arsenal and it's great to think that so many Arsenal supporters and visitors will be able to enjoy this tribute to such a great player for years to come."