The Dutchman was honoured with a permanent tribute outside the Clock End, following along from those for other Arsenal legends such as former manager Herbert Chapman, captain Tony Adams and club-record goalscorer Thierry Henry.
Bergkamp joined Arsenal from Inter Milan in June 1995, and went on to play more than 400 games for the Gunners, scoring 120 goals. The Holland forward helped win seven major trophies with Arsene Wenger's side, including the 'Invincibles' Premier League campaign of 2003/2004.
Hundreds of Arsenal supporters turned out to welcome the 44-year-old back to London, as long-serving club director Ken Friar marked the official unveiling of the statue.
"I spoke to Thierry Henry last night and he warned me about this moment, he said 'you will be fine until you have to talk a little bit, and you will be emotional', that happens to me now," said Bergkamp.
"All this makes you realise how many good years we had here and how big this club has become over the last 20 years. I was just happy to play a role in that.
"You all see me as a team player, and there is only one statue of me, but I believe it is part of a whole team that I was involved in which made me shine.
"When you think of that team, it is not only the quality players around you, it is the fantastic manager, the staff around the club.
"I would like to thank my friends and family as well, they have been there from the beginning in my career - thank you to Henrita, my wife. We made this adventure together and have four beautiful children who were all born in England.
"Last but not least, I had a very good relationship with the fans. You were very patient with me.
"In the first six or seven games of my career, a lot of people spoke about that, is he good or not? Can he do it? We had some comments from chairmen of other clubs in London, I won't mention the name!
"We proved them all wrong and are where we are now, and it is all down to the fans because you had belief in me, in the team, so this is how it ends with a beautiful statue."
Bergkamp has just started out on his coaching career at his boyhood club Ajax in Amsterdam, but in the long term would relish the opportunity to return to Arsenal.
He said: "I would, definitely. I have just started my career at Ajax as an assistant coach, being part of the Ajax philosophy, trying to get players through the system.
"We just started that, so I don't think now is the time to leave that aside and do something else, but in the future I would love to come to this country, to this league and this club especially."
Bergkamp feels Wenger's current squad can mount a serious title challenge in 2014.
He said: "I have been watching Arsenal for many years, and this season they are really (much) stronger than the last seasons.
"They can challenge for the title, but the upcoming weeks are very important for them."